Question

a line passes through the points in this table.

x	y
-24	0
-9	3
6	6
21	9

what is the slope of the line?
write your answer as an integer or simplified fraction.

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Choose two points

Let's take the first two points \( (-24, 0) \) and \( (-9, 3) \). Here, \( x_1=-24 \), \( y_1 = 0 \), \( x_2=-9 \), \( y_2 = 3 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{3 - 0}{-9 - (-24)}=\frac{3}{15}=\frac{1}{5} \). We can check with other points, e.g., \( (-9,3) \) and \( (6,6) \): \( \frac{6 - 3}{6 - (-9)}=\frac{3}{15}=\frac{1}{5} \), which confirms the slope.

Answer:

\(\frac{1}{5}\)