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

-2,-19} -12,11

1 answer

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 \(\boxed{-3}\).