Answer <u>(assuming the equation can be written in point-slope form)</u>:
![y-2 = -\frac{3}{2}(x+6)](https://tex.z-dn.net/?f=y-2%20%3D%20-%5Cfrac%7B3%7D%7B2%7D%28x%2B6%29)
Step-by-step explanation:
When knowing a point the line crosses through and its slope, you can write an equation in point-slope form, or
.
1) First, find the slope of the line. Use the slope formula
and the x and y values of the two points given, then solve like so:
![\frac{(-1)-(2)}{(-4)-(-6)}\\= \frac{-1-2}{-4+6}\\= \frac{-3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28-1%29-%282%29%7D%7B%28-4%29-%28-6%29%7D%5C%5C%3D%20%5Cfrac%7B-1-2%7D%7B-4%2B6%7D%5C%5C%3D%20%5Cfrac%7B-3%7D%7B2%7D)
Thus, the slope is
.
2) Now, use point-slope form,
. Substitute the
,
, and
for real values.
The
represents the slope, so substitute
in its place. The
and
represent the x and y values of one point the line crosses through. Any of the two points will work, and I chose (-6,2) for this answer. So, substitute -6 for
![y-(2)= -\frac{3}{2}(x-(-6)\\y-2 = -\frac{3}{2}(x+6)](https://tex.z-dn.net/?f=y-%282%29%3D%20-%5Cfrac%7B3%7D%7B2%7D%28x-%28-6%29%5C%5Cy-2%20%3D%20-%5Cfrac%7B3%7D%7B2%7D%28x%2B6%29)