Question

Write an equation in point-slope form for the line through the given point (4,-6) with the given slope m=3/5?

Answer 1

`y=mx+c`

`-6=(4xx(3)/(5))+c`

`c=-12/5-6=-42/5`

So:

`y=(3)/(5)x-42/5`

Answer 2

The point slope form comes from the definition of slope as a measure of the change in `y` for a given change in `x` in passing from point 1 to point 2, i.e.:
slope`=m=(Deltay)/(Deltax)=(y_2-y_1)/(x_2-x_1)`...........(1).
The only difference here is that you do not have 2 points but only one!
So you have: the value of `m` and the coordinates of one point, say, point 1. So we can write in (1):
`3/5=(y-(-6))/(x-4)` where the coordinates of the other point are the unknown `x,y`.
You get rearranging:
`y+6=3/5(x-4)`
`y+6=3/5x-12/5`
`y=3/5x-12/5-6`
`y=3/5x-42/5`