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!