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=(y_2-y_1)/(x_2-x_1)`

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

`m=(-9-(-7))/(-5-(-10))=(-9+7)/(-5+10)=(-2)/(5)=-(2)/(5)`

`y-(-7)=-(2)/(5)(x-(-10))`

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

`y+7=-(2)/(5)(x+10)` use distributive property

`y+7=-(2)/(5)x-4` subtract 7 from both sides

`\boxed{y=-(2)/(5)x-11}` slope-intercept form

`y=-(2)/(5)x-11` multiply both sides by 5

`5y=-2x-55` add 2x to both sides

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