Question

A line contains the points (-9,-7) and (13,-19). Find the x-value of the x-intercept.
For example, if the x-intercept is (1/3,0), record 0.33.
Write your answer solution rounded to two decimal places.

Answer 1

Answer:

x = -21.83 or (-21.83, 0)

Step-by-step explanation:

Use the given points to find the slope of the line.

$m=\frac{y2 - y1}{x2 - x1}$

(-9, -7) (13, -19)

$m=\frac{-19-(-7)}{13 - (-9)} = \frac{-12}{22} = -\frac{6}{11}$

Use the slope and one of the given points to solve the point-slope formula

$y - y=m(x-x)$

$y-(-7)=-\frac{6}{11} (x-(-9))$

$y+7=-\frac{6}{11} x-\frac{54}{11}$

$y=-\frac{6}{11} x-\frac{131}{11}$

Since you are looking for the x-intercept, set y=0 and solve for x

$0=-\frac{6}{11}x - \frac{131}{11}$

$\frac{131}{11} =-\frac{6}{11} x$

$-21.83 = x$