Question

what is the slope of the line that passes through the points (-6, 8) and (-9, 7)? write your answer in simplest form.

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

Let \( (x_1, y_1)=(-6, 8) \) and \( (x_2, y_2)=(-9, 7) \).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{7 - 8}{-9 - (-6)} \).

Step4: Simplify numerator and denominator

Simplify the numerator: \( 7 - 8=-1 \).
Simplify the denominator: \( -9 - (-6)=-9 + 6=-3 \).
So, \( m=\frac{-1}{-3} \).

Step5: Simplify the fraction

\( \frac{-1}{-3}=\frac{1}{3} \).

Answer:

\(\frac{1}{3}\)