The line slants gradually down from left to right.

The line passes through the following points:

(negative 8 comma 0)

(0 comma negative 8)

What is an equation of the graph shown?

Question

The line slants gradually down from left to right. The line passes through the following points: (negative 8 comma 0) (0 comma negative 8) What is an equation of the graph shown?

Accepted Answer

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 0 , b is the y -intercept of the line. The line shown passes through the point 0 , - 8 , so b = - 8 . The line shown also passes through the point - 8 , 0 . The slope, m , of a line passing through two points x 1 , y 1 and x 2 , y 2 can be calculated using the equation m = y 2 - y 1 x 2 - x 1 . For the points 0 , - 8 and - 8 , 0 , this gives m = - 8 - 0 0 - - 8 , or m = - 1 . Substituting - 8 for b and - 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 - 2 , not - 1 . Choice B is incorrect. This is an equation of a line with a slope of 1 , not - 1 . Choice D is incorrect. This is an equation of a line with a slope of 2 , not - 1 .

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