Question

How do I write an equation in slope intercept form, standard form, and point-slope form using two points (2,-5) and (7,12)?

Answer 1

First you find the slope, which is the amount `y` changes for every increase of `x`

Slope-intercept is of the form `y=mx+b`

Slope= `"change in y"/"change in x"` or more formally:

`m=(Deltay)/(Deltax)=(12-(-5))/(7-2)=17/5=3 2/5 or 3.4`

Now you know the slope, fill in what you know for one of the points:

`y=mx+b->-5=3 2/5 *2+b-> b=-11 4/5 or 11.8`

So the whole equation goes: `y=3 2/5 x-11 4/5->y=3.4x-11.8`

Check with the other point:

`3.4*7 - 11.8 = 12` --check!