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4 SECTWN 3.2 The Slope of a Line 157 Calculate the value of each slope m, if possible, by using the slope formula. See Example ~ (-1) 15. m = m 17. m = (-5) ~(-5) -2 - (-2) m 19. m = m = (-3) 0-(-3) 21. m = m (-2) -8 - (-8) 23. Concept Check On the basis of the figure shown here, determine which line satisfies the given description. (a) The line has positive slope. (b) The line has negative slope. (c) The line has slope 0. (d) The line has undefined slope. 1 A /v / I D 0~ 24. Which of the following forms of the slope formula are correct? Explain. A. m = yi B. m = C. m = y2 - y\ y2 ~ y\ D. m = For Exercises 25-36, fa) find the slope of the line through each pair ofpoints, if possible, and (b) based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical. See Examples 1 and 3 and FIGURE (-2,-3) and (-1,5) 26. (-4, 1) and (-3, 4) 27. (-4, 1) and (2, 6) 28. (-3, -3) and (5,6) 31. (-2,2) and (4,-1) 34. (4,-1) and (4,3) 29. (2, 4) and (-4, 4) 30. (-6, 3) and (2, 3) 32. (-3, 1) and (6, -2) 33. (5, -3) and.(5, 2) 35. (1.5,2.6) and (0.5,3.6) 36. (3.4, 4.2) and (1.4, 10.2) Brain Busters Find the slope of the line through each pair ofpoints. I Hint,3 1A /5 10 3M 1,3 land f-,t a c 1" d 39. i^) a n d fe'~9 Find the slope of each line. 41. y Printed by Dorothy Muhammad (dorothy.muhammadij!hccs.edu)on 10/17/2012 from authorized to use until 4/12/2015. Use beyond the authorized userorvalid subscription date represents a copyright violation.

5 166 CHAPTER 3 Graphs, Linear Equations, and Functions " NOW TRY ' * EXERCISE 6 Write an equation of the line passing through the point (6,-1) and (a) parallel to the line 3x 5y = 7; (b) perpendicular to the line Give final answers in slopeintercept form. If 3 (b) To be perpendicular to the line 2x + 3y = 6, a line must have a slope that is the negative reciprocal of 3, which is i. We use ( 3, 6) and slope 5 in the pointslope form to find the equation of the perpendicular line shown in FIGURE 32. y y, = 6, m = 5, x, = -3 I* - (-3)1 y, = 6, m = i, x, = -3 y - 6 = -(x + 3) y - 6 «-\ y 3 9 a* x Definition of subtraction Distributive property Add 6 = ' 2 2. A summary of the various forms of linear equations follows. FIGURE 32 NOW TRY D Forms of Linear Equations Equation Descr/pt/on When to Use y = mx + b y-y, = /n(x-x,) Ax + By = C y = <T x = a Slope-Intercept Form Slope is m. y-intercept is (0, fa).,, Point-Slope Form Slope is m. Line passes through (x,, y,). Standard Form (A, B, and C integers, A>0) Slope is - (B5* 0). x-intercept is ( 0) (>4 # 0). y-intercept is (0, f) (S * 0). Horizontal Line Slope is 0. y-intercept is (0, b). Vertical Line Slope is undefined, x-intercept is (a, 0). The slope and y-intercept can be easily identified and used to quickly graph the equation. This form is ideal for finding the equation of a line if the slope and a point on the line or two points on the line are known. The x- and y-intercepts can be found quickly and used to graph the equation. The slope must be calculated. If the graph intersects only the y-axis, then y is the only variable in the equation. If the graph intersects only the x-axis, then x is the only variable in the equation. OBJECTIVE 7 Write an equation of a line that models real data. If a given set of data changes at a fairly constant rate, the data may fit a linear pattern, where the rate of change is the slope of NOW TRY ANSWERS 6. (a) y = h - $ EXAMPLE 7 Determining a Linear Equation to Describe Real Data A local gasoline station is selling 89-octane gas for $3.20 per gal. (a) Write an equation that describes the cost y to buy x gallons of gas. The total cost is determined by the number of gallons we buy multiplied by the price per gallon (in this case, $3.20). As the gas is pumped, two sets of numbers spin by: the number of gallons pumped and the cost of that number of gallons. (b) y = - p + 9 Printed by Dorothy Muhammad (dorothy.muhammad@hccs.edu)on 10/17/2012 from authorized to use until 4/12/2015. Use beyond the authorized userorvalid subscription date represents a copyright violation.

6 qp SECTION 3.3 Linear Equations in Two Variables 171 L V J 39. Through (-5, 4); slope ^ 40. Through (7, -2); slope \ 41. x-intercept (3, 0); slope x-intercept ( 2, 0); slope Through (2, 6.8); slope Through (6, -1.2); slope 0.8 Find an equation of the line that satisfies the given conditions. See Example Through (9, 5); slope Through (-4,-2); slope Through (9, 10); undefined slope 48. Through (-2, 8); undefined slope 49. Through (~, - ); slope Through (-f, -f); slope Through ( 7, 8); horizontal 52. Through (2, 7); horizontal 53. Through (0.5, 0.2); vertical 54. Through (0.1, 0.4); vertical Find an equation of the line passing through the given points, (a) Write the equation in standard form, (b) Write the equation in slope-intercept form if possible. See Example (3,4) and (5, 8) 56. (5,-2) and (-3, 14) 57. (6, 1) and (-2, 5) 58. (-2, 5) and (-8, 1) 59. (2, 5) and (1, 5) 60. (-2, 2) and (4, 2) 61. (7,6) and (7,-8) 62. (13, 5) and (13,-1) 63. Q, -3^ and(-, -3) 64. -e) and (~ -6 Find an equation of the line that satisfies the given conditions, (a) Write the equation in slopeintercept form, (b) Write the equation in standard form. See Example Through (7, 2); parallel to 3x - y = Through (4, 1); parallel to 2x + 5y = Through (-2,-2); parallel to -x + 2y = Through (-1,3); parallel to -x + 3v = Through (8, 5); perpendicular to 2x y = Through (2, 7); perpendicular to 5x + 2y = Through (-2, 7); perpendicular to x = Through (8, 4); perpendicular to x = 3 Write an equation in the form y = mx for each situation. Then give the three ordered pairs associated with the equation for x-values 0, 5, and 10. See Example 7(a). 75. x represents the number of hours traveling at 45 mph, and y represents the distance traveled (in miles). 76. x represents the number of t-shirts sold at $26 each, and y represents the total cost of the t-shirts (in dollars). 77. x represents the number of gallons of gas sold at $3.10 per gal, andy represents the total cost of the gasoline (in dollars). 78. x represents the number of days a DVD movie is rented at $4.50 per day, and y represents the total charge for the rental (in dollars). 79. x represents the number of credit hours taken at Kirkwood Community College at $111 per credit hour, and y represents the total tuition paid for the credit hours (in dollars). (Source: x represents the number of tickets to a performance of Jersey Boys at the Des Moines Civic Center purchased at $125 per ticket, and y represents the total paid for the tickets Printed by Dorothy Muhammad (dorothy.muhammad@hccs.edu) <^Myj20a2 ifsfoffigp frclmh^tet?) 10 u s e u n t i l 4 / 1 2 / U s e subscnption date represents 'a copyright violation. beyond the authorized user or valid

7 SECTION 3.4 Linear Inequalities in Two Variables 179 o For Discussion or Writing Solve the equation in part (a) and the associated inequalities in parts (b) and (c), by graphing the left side as y in the standard viewing window of a graphing calculator. Explain your answers using the graph. 1. (a) 5x + 3 = 0 (b) 5x + 3 > 0 (c) 5x + 3 < 0 2. (a) 6x + 3 = 0 (b) 6x + 3 > 0 (c) 6x + 3 < 0 3. (a) -8x - (2x + 12) = 0 (b) -8x - (2x + 12) > 0 (c) -8x - (2x + 12) < 0 4. (a) -4x - (2x + 18) = 0 (b) -4x - (2x + 18) > 0 -(c) -4x - (2x + 18) < EXERCISES MyMathLabt. 2L Complete solution available on the Video Resources on DVD 0 Concept Check In Exercises 1-4, fill in the first blank with either solid or dashed. Fill in the second blank with either above or below. 1. The boundary of the graph ofy ^ x + 2 will be a. _ line, and the shading will be 2. The boundary of the graph ofy < x + 2 will be a. _ line, and the shading will be 3. The boundary of the graph ofy > x + 2 will be a. _ line, and the shading will be 4. The boundary of the graph ofy s x + 2 will be a _ - line, and the shading will be [3 5. How is the boundary line Ax + By = C used in graphing either Ax + By < C or Ax + By > CI [J 6. Describe the two methods discussed in the text for deciding which region is the solution set of a linear inequality in two variables. Graph each linear inequality in two variables. See Examples 1 and x + y < x - y < * - y < x + 3y > x + 4y > x + 3y > x + Ay > x - 3y > x - 5y > x + y > x + 2y > x - 3y < x - 5y < y < x 22. y < 4x Graph each compound inequality. See Example x + y < 1 and x > x - y a 2 and x > x - y > 2 and y < x - y > 3 and y < x + y > -5 and y < x - 4y < 10 and y > 2 Printed by Dorothy Muhammad (dorothy.muhammad@hccs.edu)on 10/17/2012 from authorized to use until 4/12/2015. Use beyond the authonzed userorvalid subscription date represents a copyright violation.