Question

What is the slope of the line passing through `(-4,-8); (-3,-3)`?

Answer 1

`(y+8) = 5(x+4)`

Explanation:

First you determine the slope:

`(color(blue)(x_1),color(blue)(y_1)) = (-4,-8)`

`(color(red)(x_2),color(red)(y_2))=(-3,-3)`

`color(green)m =(color(red)(y_2)-color(blue)(y_1))/(color(red)(x_2)-color(blue)(x_1))`

`color(green)m =(color(red)(-3)-color(blue)((-8)))/(color(red)(-3)-color(blue)((-4)))`

`color(green)m =(color(red)(-3)+color(blue)(8))/(color(red)(-3)+color(blue)(4)) = 5/1 = 5`

Now use the Point Slope form of a line:

`(y-color(blue)(y_1)) = color(green)m(x-color(blue)(x_1))`

`(y-color(blue)((-8))) = color(green)(5)(x-color(blue)((-4)))`

`(y+color(blue)(8)) = color(green)(5)(x+color(blue)(4))`

graph{(y+8) = 5(x+4) [-21.96, 18.04, -3.16, 16.84]}