Question

a line passes through the points in this table.

x	y
3	7
8	5
13	3
18	1

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

submit

Explanation:

Step1: Recall slope formula

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

Step2: Choose two points

Let's take the first two points \((3, 7)\) and \((8, 5)\). Here, \( x_1 = 3 \), \( y_1 = 7 \), \( x_2 = 8 \), \( y_2 = 5 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{5 - 7}{8 - 3}=\frac{-2}{5} \). We can verify with other points, e.g., \((8, 5)\) and \((13, 3)\): \( \frac{3 - 5}{13 - 8}=\frac{-2}{5} \), and \((13, 3)\) and \((18, 1)\): \( \frac{1 - 3}{18 - 13}=\frac{-2}{5} \). So the slope is consistent.

Answer:

\(-\frac{2}{5}\)