sat suite question viewer

Algebra / Linear equations in two variables Difficulty: Medium

What is an equation of the graph shown?

$y = - 2 x - 8$

$y = x - 8$

$y = - x - 8$

$y = 2 x - 8$

Back question 27 of 126 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

Explanation

Choice C is correct. An equation of a line can be written in the form $y = m x + b$ , where $m$ is the slope of the line and $left parenthesis 0 comma b right parenthesis$ is the y-intercept of the line. The line shown passes through the point $left parenthesis 0 comma negative 8 right parenthesis$ , so $b = - 8$ . The line shown also passes through the point $left parenthesis negative 8 comma 0 right parenthesis$ . The slope, $m$ , of a line passing through two points $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis x 2 comma y 2 right parenthesis$ can be calculated using the equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ . For the points $left parenthesis 0 comma negative 8 right parenthesis$ and $left parenthesis negative 8 comma 0 right parenthesis$ , this gives $m = \frac{(- 8) - 0}{0 - (- 8)}$ , or $m = - 1$ . Substituting $negative 8$ for $b$ and $negative 1$ for $m$ in $y = m x + b$ yields $y = (- 1) x + (- 8)$ , or $y = - x - 8$ . Therefore, an equation of the graph shown is $y = - x - 8$ .

Choice A is incorrect. This is an equation of a line with a slope of $negative 2$ , not $negative 1$ .

Choice B is incorrect. This is an equation of a line with a slope of $1$ , not $negative 1$ .

Choice D is incorrect. This is an equation of a line with a slope of $2$ , not $negative 1$ .