What is (-12,8) & (9,1) in point slope form?

Question

In point slope form please!!!!

Answer 1

Hi Melissa.

 

The point slope form of the equation of a line is

 

y-y₁ = m (x-x₁)

where

m is the slope

and (x₁,y₁) is one of the points given.

 

You have been given 2 points (-12,8) and (9,1).  You can call one of  them (x₁,y₁) and the other (x₂,y₂).  It doesn't matter which one is which.

 

But before we go further, we need to determine the slope.

We can do this from the points as well.

 

         y₂-y₁

m = ---------

         x₂-x₁

 

Let's say

(x₁,y₁) = (-12,8)

(x₂,y₂) = (9,1)

 

This gives us a slope of

 

        y2-y1             1-8           -7        -1
m = ---------  =  ----------  =  ----  =  ---
        x2-x1          9-(-12)        21         3

 

Now that we have everything we need

 

y-8 = (-1/3)[x-(-12)]

Distribute the -1/3

y-8 = (-1/3)x -4

 

If we add 8 to both sides we have the equation in the slope intercept form (y=mx+b)

y = (-1/3)x + 4

Answer 2

First compute the slope:

 

m = [1 - 8] / [9 - (-12)] = -7/21 = -1/3

 

We use either point in the point slope formula, so let's use (9,1).

 

y = m(x - x₀) + y₀ = (-1/3)(x - 9) + 1