Question

The slope-intercept form of the equation of a line that passes through point (-3, 8) is y = -3x + 6. What is the point-slope form

of the equation for this line?

Answer 1

Hello, I think there is an error in the problem. (-3,8) is NOT a point that y=-3x+6 passes through. I believe the slope intercept form should be y=-3x-1.

Answer:
`y-8=-3(x+3)`

Explanation:

The slope-intercept form is
`y=mx+b`. Now, the point-slope form is basically a manipulation. They are both equal to each other. The equation for point-slope form is
`y-y_(1) =m(x-x_1)`.

We can easily plug in the m of the equation.

`y-y_1=-3(x-x_1)`

Since the problem gives us a pair of coordinates, we can plug them into
`y_1` and
`x_1`.

`y-8=-3(x-(-3))`

`y-8=-3(x+3)`

It is important to check and see if this point-slope form is equal to the slope intercept form.

`y-8=-3(x+3)`

`y-8=-3x-9`

`y=-3x-1`