Question

The points (9,3) and (1,x) lie on the same line. if the slope of the line is -3, what is the value of x?

help

Answer 1

Answer: x = 27

Work Shown

rise = change in y values = x-3

run = change in x values = 1-9 = -8

slope = rise/run = -3

rise/run = -3

(x-3)/(-8) = -3

x-3 = -8*(-3)

x-3 = 24

x = 24+3

x = 27 is the answer

Let's check the answer.

The claim is the slope of the line through (9,3) and (1,27) is m = -3

The scratch work is shown below.

`\text{Given Points: }(x_1,y_1) = (9,3) \text{ and } (x_2,y_2) = (1,27)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (27 - 3)/(1 - 9)\\\\m = (24)/(-8)\\\\m = -3\\\\`

The answer is confirmed.