Complete the equation for the linear function whose graph contains the points

(−1, −2) and (3, 10).
y+? =? (x+1)

Get the slope:
( 10-(-2) )/( 3 - (-1) ) = 3

Let's use letters to represent the ?'s.
y + k = m(x + 1)

Examine the equation:
Notice that if x were to equal -1, the equation would be equal to 0.
m(-1 + 1) = m(0) = 0

If x were to be -1, then y would have to be -2 since that is one of the points provided in the problem.

So now we have:
-2 + k = 0

Solve for k:
k = 2

So I know that 2 is the only number that will work for k.

Our new equation is y + 2 = m(x + 1)

Recall point slope form:
y - y1 = m(x - x1)

Our equation is in the same form as point slope form, so we know that m in our equation represents the slope.

We found the slope at the beginning, it was 3. So plug it in:
y + 2 = 3(x + 1)

Let's test our answer by plugging in a point. Let's try (3, 10):
10 + 2 = 3(3 + 1)
12 = 12

So our answer is correct:
y + 2 = 3(x + 1) is the answer.