Question

what is the slope of this line? the line passes through points (-6, 8) and (-4, 5) on a coordinate grid. multiple - choice options: \\(\frac{3}{2}\\), \\(-\frac{3}{2}\\), 0, 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 the two points

We have points \((-6, 8)\) and \((-4, 5)\). Let \((x_1, y_1) = (-6, 8)\) and \((x_2, y_2) = (-4, 5)\).

Step3: Substitute into the formula

Calculate \( y_2 - y_1 = 5 - 8 = -3 \) and \( x_2 - x_1 = -4 - (-6) = -4 + 6 = 2 \). Then \( m = \frac{-3}{2} = -\frac{3}{2} \).

Answer:

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