Question

what is the slope of the line that passes through the points (-7, -2) and (-15, -14)? write your answer in simplest form.

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
Let \( (x_1, y_1) = (-7, -2) \) and \( (x_2, y_2) = (-15, -14) \).

Step2: Substitute values into formula

Substitute \( x_1 = -7 \), \( y_1 = -2 \), \( x_2 = -15 \), \( y_2 = -14 \) into the slope formula:
\( m = \frac{-14 - (-2)}{-15 - (-7)} \)

Step3: Simplify numerator and denominator

Simplify numerator: \( -14 - (-2) = -14 + 2 = -12 \)
Simplify denominator: \( -15 - (-7) = -15 + 7 = -8 \)
So, \( m = \frac{-12}{-8} \)

Step4: Reduce the fraction

Simplify \( \frac{-12}{-8} \) by dividing numerator and denominator by their greatest common divisor, which is 4:
\( \frac{-12 \div 4}{-8 \div 4} = \frac{-3}{-2} = \frac{3}{2} \)

Answer:

\(\frac{3}{2}\)