0.09e: Exercises - Graphs of Linear Equations

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A: Find the slope of a line given its graph

Exercise $\PageIndex{A}$: Find the Slope of a Line given its Graph

Find the slope of each line shown.

1. $This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, negative 4) and (5, negative 2).$	2. $This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, negative 5) and (2, negative 2).$	3. $This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, negative 1) and (4, 4).$	4. $This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, negative 2) and (3, 3).$
5. $This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 2) and (3, 1).$	6. $This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, negative 1) and (3, negative 3).$	7. $This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 4) and (2, negative 1).$	8. $This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 2) and (4, negative 1).$
9. $071 y=-4.jpg this is a graph of a horizontal line intersecting the y axis at (0,negative 4)$	10. $071 y=3.jpg$	11. $071 x=-1.jpg$	12. $071 x=3.jpg this is a gaph of a vertical line intersecting the x-axis at (0,3)$

Answers to odd exercises.: 1. $m=\frac{2}{5}$ 3. $m=\frac{5}{4}$ 5. $m = -\frac{1}{3}$ 7. $m = -\frac{5}{2}$ 9. $m = 0$ 11. $m$ = undefined

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B: Calculate the slope of a line given 2 points on the line

Exercise $\PageIndex{B}$: Calculate Slope given 2 points

Use the slope formula to find the slope of the line between each pair of points.

13. $(2,5),\;(4,0)$	14. $(3,6),\;(8,0)$	15. $(−3,3),\;(4,−5)$	16. $(−2,4),\;(3,−1)$
17. $(−1,−2),\;(2,5)$	18. $(−2,−1),\;(6,5)$	19. $(4,−5),\;(1,−2)$	20. $(3,−6),\;(2,−2)$

Answers to odd exercises.: 13. $m = -\frac{5}{2}$ 15. $m = -\frac{8}{7}$ 17. $m = \frac{7}{3}$ 19. $m = -1$

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C: Identify attributes given a linear equation

Exercise $\PageIndex{C}$: Identify Slope and y-intercept given a linear equation

Identify the slope and $y$-intercept of each line.

29. $y=−7x+3$	30. $y=4x−10$	31. $3x+y=5$	32. $4x+y=8$
33. $6x+4y=12$	34. $8x+3y=12$	35. $5x−2y=6$	36. $7x−3y=9$
37. $y=3$	38. $y=−2$	39. $x=−5$	40. $x=4$

Use slopes and $y$-intercepts to determine if the lines are parallel, perpendicular, or neither.

41. $y=\frac{3}{4}x−3$; $3x−4y=−2$	42. $3x−4y=−2$; $y=\frac{3}{4}x−3$	43. $2x−4y=6$; $x−2y=3$	44. $8x+6y=6$; $12x+9y=12$
45. $x=5$; $x=−6$	46. $x=−3$; $x=−2$	47. $4x−2y=5$; $3x+6y=8$	48. $8x−2y=7$; $3x+12y=9$
49. $3x−6y=12$; $6x−3y=3$	50. $9x−5y=4$; $5x+9y=−1$	51. $7x−4y=8$; $4x+7y=14$	52. $5x−2y=11$; $5x−y=7$
53. $3x−2y=8$; $2x+3y=6$	54. $2x+3y=5$; $3x−2y=7$	55. $3x−2y=1$; $2x−3y=2$	56. $2x+4y=3$; $6x+3y=2$
57. $y=2$; $y=6$	58. $y=−1$; $y=2$

Answers to odd exercises.: 29. $m=−7$; $(0,3)$    31. $m=−3$; $(0,5)$    33. $m=−\frac{3}{2}$; $(0,3)$    35. $m=\frac{5}{2}$; $(0,−3)$
37. $m = 0$; $(0,3)$ 39. slope is undefined; no y-intercept
41. parallel    43. lines are the same    45. parallel vertical lines 47. perpendicular    49. neither    51. perpendicular
53. perpendicular    55. neither    57. parallel horizontal lines

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D: Graph a line given its attributes

Exercise $\PageIndex{D}$: Graph a line given its attributes

Graph each line with the given point and slope.

71. $(2,5)$; $m=−\frac{1}{3}$	72. $(1,4)$; $m=−\frac{1}{2}$	73. $(−1,−4)$; $m=\frac{4}{3}$	74. $(−3,−5)$; $m=\frac{3}{2}$
75. $y$-intercept: $(0, 3)$; $m=−\frac{2}{5}$	76. $x$-intercept: $(−2,0)$; $m=\frac{3}{4}$	77. $(−4,2)$; $m=4$	78. $(1,5)$; $m=−3$

Answers to odd exercises.

71. $OER 165 0.9e #71.png This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (2, 5) and (5, 4).$

73. $OER 165 0.9e #73.png This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (negative 1, negative 4) and (2, 0).$

75. $OER 165 0.9e #75.png This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, 3) and (5, 1).$

77. $OER 165 0.9e #77.png This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (negative 4, 2) and (negative 3, 6).$

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E: Graph a linear equation using the slope-intercept method

Exercise $\PageIndex{E}$: Graph a linear equation

Graph the line of each equation using its slope and y-intercept.

83. $y=3x−1$	84. $y=2x−3$	85. $y=−x+3$	86. $y=−x−4$
87. $y=−\frac{2}{5}x−3$	88. $y=−\frac{3}{5}x+2$	89. $3x−2y=4$	90. $3x−4y=8$

Answers to odd exercises.

83.
$OER 165 0.9e #83.png This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 1) and (1, 2).$

85.
$OER 165 0.9e #85.png This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).$

87.
$OER 165 0.9e #87.png This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).$

89.
$OER 165 0.9e #89.png This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 2) and (2, 1).$

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8/17/2025

13. \((2,5),\;(4,0)\)	14. \((3,6),\;(8,0)\)	15. \((−3,3),\;(4,−5)\)	16. \((−2,4),\;(3,−1)\)
17. \((−1,−2),\;(2,5)\)	18. \((−2,−1),\;(6,5)\)	19. \((4,−5),\;(1,−2)\)	20. \((3,−6),\;(2,−2)\)

29. \(y=−7x+3\)	30. \(y=4x−10\)	31. \(3x+y=5\)	32. \(4x+y=8\)
33. \(6x+4y=12\)	34. \(8x+3y=12\)	35. \(5x−2y=6\)	36. \(7x−3y=9\)
37. \(y=3\)	38. \(y=−2\)	39. \(x=−5\)	40. \(x=4\)

41. \(y=\frac{3}{4}x−3\); \(3x−4y=−2\)	42. \(3x−4y=−2\); \(y=\frac{3}{4}x−3\)	43. \(2x−4y=6\); \(x−2y=3\)	44. \(8x+6y=6\); \(12x+9y=12\)
45. \(x=5\); \(x=−6\)	46. \(x=−3\); \(x=−2\)	47. \(4x−2y=5\); \(3x+6y=8\)	48. \(8x−2y=7\); \(3x+12y=9\)
49. \(3x−6y=12\); \(6x−3y=3\)	50. \(9x−5y=4\); \(5x+9y=−1\)	51. \(7x−4y=8\); \(4x+7y=14\)	52. \(5x−2y=11\); \(5x−y=7\)
53. \(3x−2y=8\); \(2x+3y=6\)	54. \(2x+3y=5\); \(3x−2y=7\)	55. \(3x−2y=1\); \(2x−3y=2\)	56. \(2x+4y=3\); \(6x+3y=2\)
57. \(y=2\); \(y=6\)	58. \(y=−1\); \(y=2\)

71. \((2,5)\); \(m=−\frac{1}{3}\)	72. \((1,4)\); \(m=−\frac{1}{2}\)	73. \((−1,−4)\); \(m=\frac{4}{3}\)	74. \((−3,−5)\); \(m=\frac{3}{2}\)
75. \(y\)-intercept: \((0, 3)\); \(m=−\frac{2}{5}\)	76. \(x\)-intercept: \((−2,0)\); \(m=\frac{3}{4}\)	77. \((−4,2)\); \(m=4\)	78. \((1,5)\); \(m=−3\)

83. \(y=3x−1\)	84. \(y=2x−3\)	85. \(y=−x+3\)	86. \(y=−x−4\)
87. \(y=−\frac{2}{5}x−3\)	88. \(y=−\frac{3}{5}x+2\)	89. \(3x−2y=4\)	90. \(3x−4y=8\)

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