Question

Find the slope of the line that passes through the points. You must show ALL work to earn full credit.
(-2,-19) and (-12,11)

Answer 1

To find the slope of the line that passes through the points \((-2,-19)\) and \((-12,11)\), we can use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, we assign the points as follows:
- \((x_1, y_1) = (-2, -19)\)
- \((x_2, y_2) = (-12, 11)\)

Now we can substitute these values into the slope formula.

1. Calculate \(y_2 - y_1\):
\[
y_2 - y_1 = 11 - (-19) = 11 + 19 = 30
\]

2. Calculate \(x_2 - x_1\):
\[
x_2 - x_1 = -12 - (-2) = -12 + 2 = -10
\]

3. Now substitute these results into the slope formula:
\[
m = \frac{30}{-10}
\]

4. Simplify:
\[
m = -3
\]

Thus, the slope of the line that passes through the points \((-2,-19)\) and \((-12,11)\) is \(\boxed{-3}\).