Hi Anthony!
To write an equation for a line given two points, you can:
1. Find the slope.
2. Use the slope and a given point to write the equation in point-slope form.
3. Solve for slope-intercept form if that is necessary.
Here's how you do it for this problem:
1. Find the slope using slope formula ("rise over run"):
m = rise/run = (y_{2} - y_{1})/(x_{2} - x_{1})
For this problem:
(x_{1}, y_{1}) = (-3,5)
(x_{2}, y_{2}) = (-2,-6)
Plug those values into slope formula:
m = (-6 - 5)/(-2 - (-3))
Watch your signs and simplify:
m = (-11)/(1) = -11
So, your slope is -11.
2. Now, you can write the line equation in point-slope form,
which looks like this:
y - y_{1} = m(x - x_{1})
Plug in the slope you found, and one of the given points. I'll use (-3,5), but you can use either.
y - 5 = -11(x - (-3))
y - 5 = -11(x + 3)
That is the equation in point-slope form.
3. You can then simplify to slope-intercept form, y = mx + b.
Use the point-slope form, and solve for y ("get y alone on one side of the equals sign"):
y - 5 = -11(x + 3)
y - 5 = -11x - 33
y = -11x - 33 + 5
y = -11x - 28
In slope-intercept form, your answer is:
y = -11x - 28
Hope this helps!