Question

What is the equation in point-slope form and slope intercept form for the line given (–1, –3) and (4, 1)?

Answer 1

Given two points `(x_1,y_1)` and `(x_2,y_2)`
the slope is `m=(y_2-y_1)/(x_2-x_1)`

For the given points `(x_1,y_1) = (-1,-3)` and `(x_2,y_2)=(4,1)`

`m=(1-(-3))/(4-(-1)) = 4/5`

Now that we have the slope we can use either of the given points to write a slope-point form for the equation:
`(y-1) = 4/5(x-4)`

The slope intercept form is
`y=mx+b`
where `b` is the y-intercept

Working with the previously developed slope-point form:
`(y-1)=4/5(x-4)=4/5x -16/5`

We obtain the slope-intercept form:
`y = 4/5x -11/5`