Answer:
-1
Step-by-step explanation:
To find the slope, I'm going to line up the points and subtract.
I will then put 2nd difference over first difference.
( -3 , 2k)
-( k , 6)
-----------------
-3-k , 2k-6
So the slope in terms of k is:
[tex]\frac{2k-6}{-3-k}[/tex].
We are also given the slope is 4 or 4/1.
This means we have the following equation to solve for k such that the slope is 4:
[tex]\frac{2k-6}{-3-k}=\frac{4}{1}[/tex]
Cross multiply:
[tex]1(2k-6)=4(-3-k)[/tex]
Distribute:
[tex]2k-6=-12-4k[/tex]
Add 4k on both sides:
[tex]6k-6=-12[/tex]
Add 6 on both sides:
[tex]6k=-6[/tex]
Divide both sides by 6:
[tex]k=-1[/tex]
So k has to have a value of -1 for the slope to be 4.
Let's check:
(-3,-2)
(-1,6)
--------Subtracting
-2,-8
So -8/-2 is 4.
The check is good and the value for k as -1 as been verified.
