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<p class="MsoNormal">Linear functions test pdf. Linear Equations a. Example 1: Evaluate f (2) for the function f ( x ) = x − 5. Find the largest possible value of the number. An equation which involves only one variable whose highest power is 1 is known as linear equation in that variable. 2014. The y-intercept is at (0, b). Worked example: slope from two points. Example The function f(x) 2x 3(1 x) is a linear function of x because it can be rewritten as Linear Equations Test (continued) Assume line I is y + 17 15 points 6) Write an equation for the line to I that passes through (-3, 6) 10 points 7) Write the equation for a line perpendicular to I 2 + 2)-linear functions. Answers to Odd-Numbered Exercises14 Chapter 3. A linear function is a function of the form . Calculate the number of litres in the reservoir after 8 hours. Transformations of Linear Functions Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. EX 3] Write an equation of the line that passes through the point ( 2 , − 1 ) with slope 1 . Modeling with tables, equations, and graphs. Writing Linear Equations (pp. Nov 21, 2023 · A linear equation is an equation with degree 1 - that is, the highest exponent on all variables in the equation is 1. 50 for each additional toothbrush made. (d) A function whose graph has a horizontal asymptote at y = 0 and no vertical asymptotes. The independent variable is x and the dependent one is y. 𝟓 +𝟑 =𝟏𝟓 b. − | | − |. Graph y = 2x. Class Notes . 68–74) 1 optional 0. Find the rate of change. These 8th grade math worksheets are supported by visuals which help students get a crystal clear understanding of the topic. The function describing the train’s motion is a linear function, which is defined as a function with a constant rate of change, that is, a polynomial of degree 1. 2: I can write linear equation in standard form. We con rm Goldreich’s conjecture: (k) queries are indeed required to -test k-linearity for any k n 2 and for any 0 < < 1 2. Learn. On questions 2-4, the student finds the slope from an equation, a graph and a table. ANS: a) Let h represent the number of hours of play time. Algebra II Word Problems: Linear Inequalities. linear relation e. 5 Matrices and Matrix Operations; 9. -19 b. When solving a system containing two linear equations there will be one ordered pair (x,y) that will work in both equations. where b is the initial or starting value of the function (when input, x = 0 ), and m is the constant rate of change, or slope of the function. The Fahrenheit temperature reading (F) is a linear function of the Celsius reading (C). Quadratic Functions have constant second differences. Unit 6 Lesson 10 linear functions test is designed to assess your knowledge and skills in working with linear functions, including graphing, solving equations, and interpreting slope and y-intercept. Lesson 3 - Domain & Range. Write y = 5 x + 7 in standard form using integers. x If the growth or decay involves increasing or decreasing by a fixed number, use a linear function. interpolate b. 12) Jeffery has grades of 93 and 81 on the first two tests of the quarter. 29 Glencoe Algebra 1. Example B: Given the linear function = ˙ − 6, solve for the x-intercept. x 4y 0 14. a rate of 50 000 litres of oil per hour. f ( x) = –2 x + 5. x y 0 0 4 12 Label Your 2. in4 4 PDF Pass 66/11/08 12:22:34 AM/11/08 12 1. People. Ch 6 Practice Test. Clarifying standard form rules. Free lessons, worksheets, and video tutorials for students and teachers. To fi nd the inverse of a function algebraically, switch the roles of x and y, and then solve for y. 92. graph linear function using different methods; and 4. The General Form of a basic linear equation is: ax b c. The graph is not a function because it fails the vertical line test. The solution to an equation is the set of all values that check in the At this level focus on linear and exponential functions. Modeling with linear equations: snow. The cost increases by $4. (b) Write the equation as a linear function. The graph has a one-to-many mapping of x-values to y-values. LINEAR ALGEBRA (MATH 110. Example The function f(x) 2x 3(1 x) is a linear function of x because it can be rewritten as Learn. Lesson 6 - Function Notation. b) Use the value of x to find y in the equation 11 = y − x. 1. 14. c. x y 0 4 1 3 2 2 4 0 7. (4) Discussion or collaboration is not permitted. 15. Before proving this theorem, we make We can solve equations of the form f(x) = k by sketching y = f(x) and the horizontal line. Theorem (Soundness of BLR). Example The graph of y 2x 1 is a straight line with gradient m = 2 and y-intercept (0, –1). Linear equations word problems: volcano. R X sAcljlt FrTi\guhKtGsW jrWeyszeMrvvQeNd[. What are the x and y intercepts of the following linear equation. Also note that the functions f and f 1 have the effect of “undoing” each other. A linear function is a function whose graph is a line. The graph of an inverse function is a refl ection of the graph of the original function. The company decides to add a one-time $10 fee for cleaning. Cost ($) PARTS OF LINEAR EQUATIONS(A1. Topics in this unit include: Graphing reciprocal linear and quadratic functions, quotients of linear functions, combinations of functions, solving rational equations and inequalities. Linear Equations(pp. extrapolate c. Find here an unlimited supply of printable worksheets for solving linear equations, available as both PDF and html files. Multiple Choice Identify the choice that best completes the statement or answers the question. A function g is defined by the rule g(x) = f(x − 2). ELEMENTARY MATRICES; DETERMINANTS15 Representing Linear Functions. Linear functions A linear function is a function of the form f(x) = ax+b, where a and b are real numbers. 02 Use piece-wise defined functions to model and solve problems; justify results. This follows chapter 1 of the principles of math grade 10 McGraw Hill While practicing this sheet keep in mind the basic concept on linear equations. 2) 2, , , 3 , 3 6 yx 3) What is the formula for finding the slope of a line? 4) The slope of a vertical line is _____. SOLUTION If you have more than one linear equation, it’s called a system of linear equations, so that x+y =5 xy =3 is an example of a system of two linear equations in two variables. Identify x intercept. At the start of the operation, there were 400 000 litres in the reservoir. Linear graphs word problems. Positive & negative slope. 7 Linear Functions Linear functions are functions that have straight line graphs, so: A linear function of x has the standard form f(x) mx c. Now dilate f(x) by a scale factor of 6. Finding the Inverse of a Linear Function Find the inverse of f(x) = 3x − 1. PR4 TOP: Patterns and Relations (Variables and Equations) KEY: Procedural Knowledge 22. x− 2y= −16 2) 13x− 11y= −12 3) 9x− 7y= −7 4) x− 3y= 6 5) 6x+ 5y= −15 6) 4x− y= 1 7) 11x− 4y= 32 8) 11x− 8y= −48. Exercises 10 2. Lisa is 6 years older than twice her sister's age. You can customize the worksheets to include one-step, two-step, or multi-step equations, variable on both sides, parenthesis, and more. y = k on the same axes. Identify the domain and range of the function. Intro to slope. 3. Set of inputs; set of outputs; set x to the domain value and calculate y. The variety of problems that these worksheets offer helps students approach these concepts in an engaging and fun manner. Then graph. 5 Solving Linear Inequalities by Using Multiplication and Division Relations & Functions Textbook: Student Workbook (blank copy) Class Notes: Lesson 1- Relations & Functions. 4: 5, 1 , 6, 2 , 7, 3 , 8, 4. If C = 0 when F = 32 and the readings are the same at -40˚, express F as a function of C. Class Notes. 5 Absolute Value Transformations 2014. P is the constant term or the y-intercept and is also the value of the dependent variable. x y -5 0 5 10 Free lessons, worksheets, and video tutorials for students and teachers. Name: _ Class: _ Date: _ Linear Equations Find the slope of the line. To Solve: the goal is to write the equation in the form variable = constant. variable d. ca Relations and Functions Practice Exam 173. 2x y 5 12. Determine whether the following function is increasing or decreasing. D. Graph the linear equation e. Worked example: slope from graph. Graph some of the lines in each pencil. 3 Modeling with Linear Functions. d. Answers to Odd-Numbered Exercises8 Chapter 2. pdf. What do you think will happen if we fix b and vary a? Let us try some examples. b) Interpret the constants, coefficients, and bases in context of the problem. 1 FUNCTIONS AND FUNCTION NOTATION 3 • Graph: The data from Table 1. 63–67) 1 optional 0. As previously described, a linear equation can be defined as an equation in which the highest exponent of the equation variable is one. The process of setting a function equal to 0 to get the x-intercept is important in future lessons as this is the 1 x. Linear Functions Practice Test. The linear equation that represents this table of values is _____. Some examples of linear equations include: 2 x − 3 = 5 2 x = 8 y = 9 x − 3 LINEAR EQUATIONS WORKSHEET #1 Exercise 1 Exercise 2 Exercise 3 . 2x 5y 10 15. Converting from slope-intercept to standard form. Give today and help us reach more students. (2) This midterm should be completed in 3 hours. Relations and Functions. We can divide or multiply both sides of the equation by the same non-zero integer. If f is δ-far from linear, then Pr[BLR test rejects f] ≥ min (2 9, δ 2) ≥ 2δ 9. Background 3 1. ca Relations and Functions Practice Exam Definition: Linear Function. linear equation f. In 2010 the population was 55, 000 55, 000. Lesson 2. Rita graphs her progress through the book by putting the time in hours t on the horizontal axis and chapters remaining C on the vertical axis. All lines with the same slope, but different intercepts, are also called a “pencil,” a pencil of parallel lines. math10. Rearrange the following standard form linear equation in the slope-y-intercept form. Solutions to Practice Test Lesson 4 Using Linear Models. Problems 7 1. You can create printable tests and worksheets from these Grade 9 Linear Equations questions! Select one or more questions using the checkboxes above each question. This is a 3-page linear functions test containing 22 questions (some with multiple parts). The cyclist can only ride until 8:00 P. Lisa is 12. Math 113 – Linear Functions Practice Test (1) Define the x and y intercepts of the line 6x 3y 18 x- intercept: _____ y-intercept: _____ (2) Complete the table of values for the line 4x 3y 36 (3) Graph the line that contains the point (2,3) and has a slope of 3. 4 Chapter 1 Solving Linear Equations 1. 7 in standard form using integers. (e) Draw the graph. It has one independent and one dependent variable. 201) FINAL EXAM - DECEMBER 2015 Name: Section number/TA: Instructions: (1) Do not open this packet until instructed to do so. 5 optional Learn. Linear functions • Time allowed: 45 minutes • Part A: 20 multiple-choice questions (20 marks) • Part B: 6 free-response questions (30 marks) Part A 20 multiple-choice questions 1 mark each: 20 marks Circle the correct answer. Example 1 Graph. illustrate a linear function; 2. Intro to linear equation standard form. Explain what the rate of change means for the situation. dollars, D. M. Graphing a linear equation: 5x+2y=20. f(x) = mx + b. –5x + 10y = 60. 5 Absolute Value Equations and Functions 2014. Unit 1: Piecewise Functions. 7 d. Objective 2. This follows chapter 3 of the grade 12 Advanced Functions McGraw Hill textbook and Part 1. exponential ,QJURZWKDQGGHFD\SUREOHPV WKDWLV SUREOHPVLQYROYLQJDTXDQWLW \LQFUHDVLQJRUGHFUHDVLQJ KHUH¶VKRZWRGHFLGH whether to choose a linear function or an exponential function. If a vertical line intersects the graph more than once, it fails the test and is not a function. c) Use the values of x and y to find m in the equation 2m + y = 3(x − 5). For example, consider the following system of equations: 4x 1 5x 2 = 13 2x 1 + 3x 2 = 9: This is two equations and two variables, so as you know from high school algebra, you can nd a unique solution for x 1 and x 2 (unless the equations are Our mission is to improve educational access and learning for everyone. ____. Then graph. Nov 13, 2014 · Writing and Graphing Linear Equations Test (Take Home Test – due November 17th, 2014) You must show work to get the credit. 10. Solve linear equations using multiplication and division. Sketch the graph using the intercepts. fails the vertical line test. 9. Introduction to Exponential Functions; Compounding in Finance, Continous Compounding and the Number \(e\) Review Percent Change; Gist of Exponential Functions; 4 Logarithmic Functions. There are two equations, and each equation has the same two variables: x and y. A car rental store rents cars for $20 a day. Lesson 4 - Graphing in a Domain. Standard form review. Lesson 5 - Graphing Continuous + Discrete Data + Vertical Line Test. ARITHMETIC OF MATRICES9 2. {( 2,3),(0,4),(3,7),( 4, 5),( 2,0)− −− −} b. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. 75–80) 1 optional 0. Write the standard form of the equation of the line through the given point with the The quadratic function f is defined by f (x) = 3x2 – 12x + 11. When x = 0, q is the coefficient of the The completeness of this test is 1, because obviously a linear function passes with probability 1. The table shows the cost of a ski rental package for a given number of people. Assume f(x) 1 2 x 3. The cost increases by $9. The rate of change is constant in each table. The function f(x) = 20x represents the daily rental fee for x days. It is used to find the element in the range that will correspond the element in the domain. Linear functions can be written in the slope-intercept form of a line. Analyzing the soundness is the interesting part; the answer is given by the following theorem. Linear Functions Practice Quiz. The worksheets suit pre-algebra and algebra 1 courses (grades 6-9). Problems 12 2. 2014 A Review Solutions . There are several ways to represent a linear function, including word form, function notation, tabular form, and graphical form. Slope (pp. 2) A town’s population increases at a constant rate. Find the function g for the translated graph, giving your answer in the form g (x) = 3(x – p)2 + q. {( 3,2),(0,5),(2,5),(0, 3),(3, 2)− − −} d View Test prep - Algebra 1 linear equations test. Determine whether the following algebraic equation can be written as a linear function. 5 Solving Linear Inequalities by Using Multiplication and Division LOC: 9. Our results. 2. The solution to the equation f(x) = k is found by determining the x-values of any points of intersection of the two graphs. For example, consider the following system of equations: 4x 1 5x 2 = 13 2x 1 + 3x 2 = 9: This is two equations and two variables, so as you know from high school algebra, you can nd a unique solution for x 1 and x 2 (unless the equations are Answers to Functions, Domain, and Range Review. A sequence can be thought of as a function, with the input numbers consisting of the integers, and the output numbers being the terms of the sequence. 10) Twenty more than a number is less than twice the same number. 4. MATRICES AND LINEAR EQUATIONS 1 Chapter 1. Chapter 4. 00 for each additional 3 toothbrushes Linear functions help us understand and analyze relationships between variables that can be represented by straight lines. Worksheet to accompany part 1. Make up a function that ts the listed conditions: (a) A function whose domain is all reals except 3. -11 c. (b) The graph of f is translated 3 units in the positive x-direction and 5 units in the positive y-direction. 6 Solving Systems with Gaussian Elimination; 9. g(x) 3x 3 FOA/Algebra 1 Unit 5: Comparing Linear, Quadratic, and Exponential Functions Notes 3 Identifying Types of Functions from a Table Remember with linear functions, they have constant (same) first differences (add same number over and over). f x ax b( )= +. Note that the domain of f is equal to the range of f 1, and vice versa, as shown in Figure 1. Calculating slope from tables. Background 9 2. 19 2. Lesson 6 Families of Functions Model and solve, concretely, pictorially and symbolically, problems that can be represented by one-step linear equations of the form x + a = b, where a and. 1 Lesson What You Will Learn Solve linear equations using addition and subtraction. 3A) 9. The graph of a linear equation is a graphical view of the set of all points that make the equation true. 1 Systems of Linear Equations: Two Variables; 9. A term may be used more than once or not at all. Topics in this unit include: solving linear systems by graphing, substitution, elimination, and solving application questions. All of the above are true. S. 1) g(x) = 4 − 3 2 x f (x) = 1 2 x + 3 2 No 2) g(n) = −12 − 2n 3 f (n) = −5 + 6n 5 No 3) f (n) = −16 + n 4 g(n) = 4n + 16 Yes 4) f (x) = − 4 7 x − 16 7 g(x) = 3 2 x − 3 2 No 5) f (n) = −(n + 1)3 g(n) = 3 + n3 No 6) f (n) = 2(n − 2)3 g(n) = 4 + 3 Inverse Functions MULTIPLE CHOICE. 11. Ordered Try the following test: Linear Equations Find the linear function f which corresponds to each graph shown below. 11) 9 less than a number is at most that same number divided by 2. Relations & Functions Textbook: Student Workbook (blank copy) Class Notes: Lesson 1- Relations & Functions. 3) f(x) = 7x + 8 A) f-1(x) = x - 8 7 B) f-1(x) = 7x - 8 7 C) f-1(x Choosing linear vs. Linear graphs word problem: cats. Write the slope-intercept form of the equation of each line. 1 Solve for x: 4 1 5 a: 5 a: 5 2 1 1 1 2 3 Solve for x: 60 4) Solve for x: b d f b d f h b 4(2x 3) 2) Jun 20, 2020 · Linear algebra provides a way of compactly representing and operating on sets of linear equations. (𝑥)=1 3 15. 37. They then filled the reservoir at. B. Unit 3 Test Date: _____Block: _____ Make a table and graph the function for Write a rule for the function. coefficient LINEAR FUNCTIONS . For example, to solve x 3 = 2 we sketch y = x 3 and. 4x 3y 9 0 . Does the graph represent a function that has an inverse function? 1) x y A) No B) Yes 1) 2) x y A) No B) Yes 2) Find the inverse of the one-to-one function. Find the slope of a line that passes through the points (5, 4) and (-2, -1) 3. 8875 Euros, write a linear function that represents the number of Euros, E, in terms of U. a) Solve for x in the equation x + 9 = 16. Equations that are functions can be written in a form called function notation. Specific Outcome. Lesson 7: Interpreting Graphs. LINEAR FUNCTIONS PRACTICE TEST Determine if the given ordered pair is a solution to the function: 3 2 8xy 1) 3,4 Complete the given ordered pairs so that each ordered pair satisfies the given equation. 1) 3. Graph the function and interpret the slope and m-intercept. \ B FM[akd^eT \wfint[hu OIFnIfQiJnliNtSeY ^Ablogwemb]roao y1f. ____ 1. The number m of miles a long-distance cyclist travels during today’s ride can be modeled by the function m(t) =12t+40, where t represents the number of hours since a noon rest stop. Linear function example: spending money. The best statement regarding the graph shown is: y = f(x) www. Rita reads a book at a steady pace. describe the domain, range, intercepts, slope and the table of values of a linear function; 3. 2 x. (d) Identify the y-intercept. b. Slope review. A linear function models the cost based on the number of toothbrushes made. g(x) 6x 3 b. (c) A function whose graph has vertical asymptotes at 2 and 5 and a horizontal asymptote at 1. Exercises 4 1. 7 Interpreting Graphs of Linear Functions. Before the Test 3-2 Solving Linear Equations 00ii_0vi_ALG1SN_BKFM_SE_890844. • Graph parallel and perpendicular lines. 7 Solving Systems 13) Answer the following questions based on the linear equation a. 3 10. Here, a represents the gradient of the line, and b represents the y-axis intercept (which is sometimes called the vertical intercept). 1 Homework Answers: 1. Write the rule for g(x) after the transformation. The line of refl ection is y = x. Find the slope and yFind the slope and y-intercept. Find the slope and y-intercept. 2 x + 3 y = 7. Grade 10. a. 3 Systems of Nonlinear Equations and Inequalities: Two Variables; 9. (b) A function whose range is everything except 0. C. Definition: A linear equation in one unknown is an equation in which the only exponent on the unknown is 1. The graph may not written as y = f(x). Match the correct term to each of the following descriptions. Every input has OAOO output; find an x with more than one y / vertical line test. f x x. (c) Identify the slope. Topic TesT 1 Which one of these is not a linear function? A = + y 23x 4 B 2x + 3y − 4 = 0 c x 4 y = D 2 y x = 7 Linear Functions Linear functions are functions that have straight line graphs, so: A linear function of x has the standard form f(x) mx c. Use linear equations to solve real-life problems. EnrichmentPencils of LinesAll of the lines that pass through a single point in the same plane are called a pencil of lines. 5 optional • Identify linear equations and functions. 1 For each of the following equations, (a) Write the equation in slope-intercept form. the given domain. A solution of a system of equations is a point that is a solution of each of I. Linear equation worksheets are a great resource for students to practice a large variety of problems. Write and then solve an equation to determine the age of Lisa's sister. 13 The graph below represents function f. 2 Systems of Linear Equations: Three Variables; 9. identify the parameters c. OpenStax is part of Rice University, which is a 501 (c) (3) nonprofit. 5. ©v ]2S0V2]0K rKSuitoaA XSFoufgtYwTaDrceD OL^L`CC. DAY TOPIC ACTIVITY 1 Monday, August 24 Function: yes/no Looking at and sketching Lesson 5: Vertical Line Test. {( 4,5),(3,0),( 2,0),(6, 2),( 3, 4)− − − −−} c. Lesson 2 - Graphing Relations. Which statement about the rate of change of this function is true? A. 2014 Absolute Value Test Review. Linear Function Graph has a straight line whose expression or formula is given by; y = f (x) = px + q. Lesson 5 Absolute Value Functions and Graphs. In other words, when you form the composition of f with f 1 or the composition of f 1 with f, you obtain the identity function. 3. Confirm by graphing with technology. Find the smallest possible value of the number. • Write linear equations in standard form and graph them. 2. Specifically, question #1 gives the student a graphed line and asks them to identify the slope, x-intercept and the y-intercept. a) Solve using tables, graphs and algebraic properties. pdf from MATH 101 at Naperville Central High School. f ( x) = 7 x + 9. Function Inverses Date_____ Period____ State if the given functions are inverses. The graph of any When graphing a linear function, there are three basic ways to graph it: 1) By plotting points (at least 2) and drawing a line through the points 2) Using the initial value (output when x= 0) and rate of change (slope) 3) Using transformations of the identity function f(x) =x. SOLUTIONS - Pretest Ch. 1) Find the area of a triangle bounded by the y y axis, the line f(x) = 10 − 2x f ( x) = 10 − 2 x, and the line perpendicular to f f that passes through the origin. 3x y 6 13. Grade 10 Math Test Solutions: Unit 1 - Linear Systems Unit | JensenMath. We can add or subtract the same number to both sides of the equation. 5. Lesson 1 - Illustrating and Graphing a Linear Function After going through this module, you are expected to: 1. Logarithmic Functions; Gist of Logarithmic REF: 6. Write y = 2 x +. (Total 6 marks) A system of equations is a collection of two or more equations with a same set of unknowns. b) h 7 PTS: 1 DIF: Moderate REF: 6. Then click the add selected questions to a test button before moving to another page. 4. Write the equation of a line with the new m and b. 4 Partial Fractions; 9. Linear equations word problems: earnings. Then give the range of Jan 12, 2006 · 1. Fur-thermore, we prove Goldreich’s conjecture by showing that the problem of distinguishing k-linear and (k+ 2)-linear functions also requires (k) queries. 1. Solve problems that involve systems of linear equations in two variables, graphically and algebraically. Find the slope of a line that passes through the points (-6, 2) and (4, 3) 2. SYSTEMS OF LINEAR EQUATIONS3 1. If you need b, plug m and an ordered pair (x, y) into the slope intercept formula and solve for b. (a) Write f in the form f (x) = 3(x – h)2 – k. Choose the one alternative that best completes the statement or answers the question. Example A: Given the linear function = −2 8 , solve for the x-intercept. The equation will look like: y = mx + b Vertical Line Test - is a test to see if the graph represents a function. Piecewise Defined Functions Activity; Gist of Domain, Range and Piecewise Defined Functions; 3 Exponential Functions. a) -19 b) 21 4) a) -39 b) 1 5) yes; All real numbers for both: D={ x| x}, R={ y| y} Unit 1: Linear Relations . Introduction to Systems of Equations and Inequalities; 9. Fitting a line to data. Linear Functions Test. (3) Notes, the textbook, and digital devices are not permitted. Complete the table: d. 5 optional • Find and use the slope of a line. in4 4ii_0vi_ALG1SN_BKFM_SE_890844. QUICK LINKS TO TOPICS Points on the Cartesian Plane Slope of a Line Equation of a Line (y=ax+b) • converse is true: any linear function f : Rn → Rm can be written as f(x) = Ax for some A ∈ Rm×n • representation via matrix multiplication is unique: for any linear function f there is only one matrix A for which f(x) = Ax for all x • y = Ax is a concrete representation of a generic linear function Linear functions and examples 2–4 Linear Functions Practice Test. This free textbook is an OpenStax resource written to increase student access to high-quality, peer-reviewed learning materials. 36. If you need m, plug the points into the slope formula. Jun 20, 2020 · Linear algebra provides a way of compactly representing and operating on sets of linear equations. If f(x) 3x 4, what is f(5)? a. Since the Writing Linear Equations Date________________ Period____. The cost increases by $1. What is the value of x when =−3? f. -intercept. Solving Linear Equations by Adding or Subtracting An equation is a statement that two expressions are equal. Graphing a line given point and slope. 1 are plotted in Figure 1. 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