Question

what is the slope of this line? (with a coordinate grid and a blue line plotted on it, with x-axis from -24 to 24 and y-axis from -24 to 24, grid lines at intervals of 3, and the line passing through points like (3,0), (0,-9), etc.)

Explanation:

Step1: Identify two points on the line

We can see that the line passes through the points \((3, 0)\) and \((0, -9)\) (or other pairs, but these are clear). Let's take \((x_1, y_1) = (3, 0)\) and \((x_2, y_2) = (0, -9)\).

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 \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the values: \(m=\frac{-9 - 0}{0 - 3}=\frac{-9}{-3}= 3\).
Alternatively, we can take another pair like \((6, 9)\) and \((3, 0)\). Then \(m=\frac{9 - 0}{6 - 3}=\frac{9}{3}=3\).

Answer:

The slope of the line is \(3\).