Question

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

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 8)\) and \((-32, 0)\). Let's denote \((x_1, y_1) = (-32, 0)\) and \((x_2, y_2) = (0, 8)\).

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 \(x_1, y_1, x_2, y_2\) into the formula:
\(m=\frac{8 - 0}{0 - (-32)}\)

Step3: Simplify the expression

First, simplify the numerator and the denominator:
The numerator \(8 - 0 = 8\)
The denominator \(0 - (-32)=0 + 32 = 32\)

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

Step4: Reduce the fraction

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

Answer:

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