Question

The graph shows the location of all solutions for some linear equation. The coordinates of two of the points are labeled. Which linear

equation matches this graph?
A)
x + y = 6
B)
y = 2x + 4
3x + y - 9
D
y = -2(x - 5) -6

Answer 1

Option D

Explanation:

Let the equation of the line given in the graph is,

y = mx + b

Here, m = Slope of the line

b = y-intercept

From the graph attached,

y-intercept = 4

Since, slope of the line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` is given by,

m =
`(y_2-y_1)/(x_2-x_1)`

Therefore, slope of the line passing through (-2, 8) and (5, -6) will be,

m =
`(8-(-6))/(-2-5)`

m =
`-(14)/(7)`

m = -2

Therefore, equation of the line will be,

y = -2x + 4

Equations given in the options A, B, and C are not matching with our equation.

Simplify the equation given in Option D,

y = -2(x - 5) -6

y = -2x + 10 - 6

y = -2x + 4

Therefore, Option D is the answer.