Question

what is the slope of this line? (with a coordinate grid and a line plotted)

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 18)\) (the y-intercept) and \((12, 36)\) (we can also use other points, but these are easy to identify).

Step2: Use the slope formula

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1) = (0, 18)\) and \((x_2, y_2) = (12, 36)\). Then:
\[
m = \frac{36 - 18}{12 - 0} = \frac{18}{12} = \frac{3}{2} = 1.5
\]
We can also check with another pair of points, say \((-12, 0)\) and \((0, 18)\). Then:
\[
m = \frac{18 - 0}{0 - (-12)} = \frac{18}{12} = \frac{3}{2} = 1.5
\]

Answer:

\(1.5\) (or \(\frac{3}{2}\))