Question

what is the slope of a line that passes through the points (5,-4) and (-3,8)?
32
$\frac{-3}{2}$
$\frac{2}{3}$
-12

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 \((x_1, y_1) = (5, -4)\) and \((x_2, y_2) = (-3, 8)\).

Step3: Substitute into formula

\( m = \frac{8 - (-4)}{-3 - 5} = \frac{8 + 4}{-8} = \frac{12}{-8} = -\frac{3}{2} \). Wait, wait, let's check again. Wait, \( y_2 - y_1 = 8 - (-4) = 12 \), \( x_2 - x_1 = -3 - 5 = -8 \). So \( \frac{12}{-8} = -\frac{3}{2} \). Wait, but looking at the options, there is \(-\frac{3}{2}\) (assuming the second option is \(-\frac{3}{2}\)). Wait, maybe I misread the options. Let me re-express: the slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1}\). So with \((5, -4)\) and \((-3, 8)\), \( y_2 - y_1 = 8 - (-4) = 12 \), \( x_2 - x_1 = -3 - 5 = -8 \). Then \( \frac{12}{-8} = -\frac{3}{2} \). So the correct option should be the one with \(-\frac{3}{2}\) (the second option, assuming the second option is \(-\frac{3}{2}\)).

Answer:

The option with \(-\frac{3}{2}\) (assuming it's the second option, e.g., B. \(-\frac{3}{2}\))