Question

How do you write the equation of a line in point slope form and slope intercept form given points (3, -8) (-2, 5)?

Answer 1

Given the points `(3,-8)` and `(-2,5)`
both the point-slope form and the slope-intercept form require that we first determine the slope.

The slope can be calculated as
`m = (Delta y)/(Delta x) = (5-(-8))/(-2-3) = - 13/5`

Using the slope `m=-13/5` and the point `(3,-8)`
the slope-point form (`y-y_1 = m(x-x_1)`) is

`y-(-8) = -13/5(x-3)`
or
`y+8 = -13/5(x-3)`

The slope-point form can be converted into the slope-intercept form (`y=mx+b`) by some minor re-arranging of terms:
`y+8 = -13/5(x-3)`

`rarr y = -13/5 x +39/5 -8`

`rarr y = -13/5x -1/8`