Question

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

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, 12)\) and \((32, 4)\). Let \((x_1, y_1) = (0, 12)\) and \((x_2, y_2) = (32, 4)\).

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:
\(m=\frac{4 - 12}{32 - 0}\)

Step3: Simplify the expression

First, calculate the numerator: \(4 - 12=-8\)

Then, calculate the denominator: \(32 - 0 = 32\)

So, \(m=\frac{-8}{32}\)

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 8:
\(m=\frac{-8\div8}{32\div8}=\frac{-1}{4}\)

Answer:

\(-\frac{1}{4}\)