Question

find the slope of the line graphed below.

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: \((2, 2)\) and \((4, -3)\). Let's denote \((x_1, y_1) = (2, 2)\) and \((x_2, y_2) = (4, -3)\).

Step2: Use the slope formula

The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the values of \(x_1, y_1, x_2,\) and \(y_2\) into the formula:
\[
m = \frac{-3 - 2}{4 - 2}
\]

Step3: Simplify the numerator and the denominator

First, calculate the numerator: \(-3 - 2 = -5\)
Then, calculate the denominator: \(4 - 2 = 2\)
So, the slope \(m = \frac{-5}{2}\)

Answer:

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