Question

determine the slope of the line through the given points.
(2, 1) and (-4, 5)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the slope is . (type an integer or a simplified fraction.)
b. the slope is undefined.

Explanation:

Step1: Recall slope formula

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

Step2: Identify coordinates

Let \((x_1, y_1) = (2, 1)\) and \((x_2, y_2) = (-4, 5)\).

Step3: Substitute into formula

Substitute values: \( m = \frac{5 - 1}{-4 - 2} \).

Step4: Simplify numerator and denominator

Numerator: \( 5 - 1 = 4 \). Denominator: \( -4 - 2 = -6 \). So \( m = \frac{4}{-6} \).

Step5: Simplify the fraction

Simplify \( \frac{4}{-6} = -\frac{2}{3} \).

Answer:

A. The slope is \(-\frac{2}{3}\).