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

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Complete the equation of the line through ( −

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10.03.2022

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

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