Question

Find the slope of the line that passes through the points. You must show ALL work to earn full credit.

-2,-19} -12,11

Answer 1

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

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

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

Now, we substitute the values into the slope formula:

1. Identify the coordinates:
\[
x_1 = -2, \quad y_1 = -19, \quad x_2 = -12, \quad y_2 = 11
\]

2. Substitute into the formula:
\[
m = \frac{11 - (-19)}{-12 - (-2)}
\]

3. Simplify the numerator:
\[
11 - (-19) = 11 + 19 = 30
\]

4. Simplify the denominator:
\[
-12 - (-2) = -12 + 2 = -10
\]

5. Now we have:
\[
m = \frac{30}{-10}
\]

6. Simplify the fraction:
\[
m = -3
\]

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