Question

a line passes through the points in this table.

x	y
-4	-18
0	2
1	7
3	17

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 given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Choose two points

Let's take the points \((0, 2)\) and \((1, 7)\) (we can choose any two points from the table). Here, \( x_1 = 0 \), \( y_1 = 2 \), \( x_2 = 1 \), \( y_2 = 7 \).

Step3: Calculate the slope

Substitute into the slope formula: \( m=\frac{7 - 2}{1 - 0}=\frac{5}{1} = 5 \). We can verify with other points, e.g., \((-4, -18)\) and \((0, 2)\): \( m=\frac{2 - (-18)}{0 - (-4)}=\frac{20}{4}=5 \), which confirms the slope.

Answer:

\( 5 \)