Question

what is the slope of the line that passes through the points (-2,6) and (-12,2)? 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 \((x_1, y_1)=(-2, 6)\) and \((x_2, y_2)=(-12, 2)\).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{2 - 6}{-12 - (-2)} \).

Step4: Simplify numerator and denominator

Simplify the numerator: \( 2 - 6=-4 \).
Simplify the denominator: \( -12 - (-2)=-12 + 2=-10 \).
So, \( m=\frac{-4}{-10} \).

Step5: Reduce the fraction

Simplify \(\frac{-4}{-10}\) by dividing both the numerator and denominator by their greatest common divisor, which is 2. So, \( \frac{-4\div2}{-10\div2}=\frac{2}{5} \).

Answer:

\(\frac{2}{5}\)