Question

Complete the equation of the line through ( − 1 0 , − 7 ) (−10,−7) and ( − 5 , − 9 ) (−5,−9).

Answer 1

The point-slope form:

$y-y_1=m(x-x_1)$

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-10, -7) and (-5, -9). Substitute:

$m=\dfrac{-9-(-7)}{-5-(-10)}=\dfrac{-9+7}{-5+10}=\dfrac{-2}{5}=-\dfrac{2}{5}$

$y-(-7)=-\dfrac{2}{5}(x-(-10))$

$\boxed{y+7=-\dfrac{2}{5}(x+10)}$    point-slope form

$y+7=-\dfrac{2}{5}(x+10)$      use distributive property

$y+7=-\dfrac{2}{5}x-4$     subtract 7 from both sides

$\boxed{y=-\dfrac{2}{5}x-11}$      slope-intercept form

$y=-\dfrac{2}{5}x-11$           multiply both sides by 5

$5y=-2x-55$      add 2x to both sides

$\boxed{2x+5y=-55}$      standard form