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: $y-8=-3(x+3)$

Step-by-step 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.

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

$y-8=-3x-9$

$y=-3x-1$