Question

what is the slope of the line that passes through the points (-1, -3) and (-19, -18)? 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 given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

Let \( (x_1, y_1)=(-1, -3) \) and \( (x_2, y_2)=(-19, -18) \).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{-18 - (-3)}{-19 - (-1)} \).
Simplify the numerator and denominator: \( -18 - (-3)=-18 + 3=-15 \), \( -19 - (-1)=-19 + 1=-18 \).
So \( m=\frac{-15}{-18} \).

Step4: Simplify the fraction

Simplify \( \frac{-15}{-18} \) by dividing numerator and denominator by their greatest common divisor, which is 3. \( \frac{-15\div3}{-18\div3}=\frac{5}{6} \).

Answer:

\(\frac{5}{6}\)