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Question
I sure could use your help.

Find the slope-intercept form of the equation of the line that passes through (-1,2)and (3,-10)

Thanks!

Answer
Hi Kaitlin, I will be happy to help.

There are three steps to finding the equation
1) Find the slope
2) Use point slope form to come up with an equation
3) Put the equation in slope intercept form

Step 1
The formula to find slope is
m = (y1 - y2)/(x1 - x2)
Here, (-1, 2) is (x1, y1) and (3, -10) is (x2, y2)
So, using the slope formula, gets
m = (2 - -10)/(-1 - 3)
m = 12/(-4)
m = -3

Step 2
Point slope form
y - y1 = m(x - x1)
Either point can be used for (x1, y1) but since (-1, 2) was used for (x1, y1) for finding the slope, we'll use it again here.
y - 2 = -3(x - -1)

Step 3
Solve for y to put the equation in slope-intercept form
y - 2 = -3(x - -1)
y - 2 = -3(x + 1)      Simplifying by changing subtracting a negative to adding a positive
y - 2 = -3x - 3         Distributing the -3
y = -3x - 1          Solving for y by adding 2 to both sides

Therefore, in slope-intecept form, the equation is

y = -3x - 1

This can be double checked by plugging each point in for (x, y) and making sure the left side of the equation is equal to the right side

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