Question

a line passes through the points in this table.

x	y
-8	2
-4	5
4	11
16	20

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 first two points \((-8, 2)\) and \((-4, 5)\). Here, \( x_1=-8 \), \( y_1 = 2 \), \( x_2=-4 \), \( y_2=5 \).

Step3: Calculate the slope

Substitute into the formula: \( m=\frac{5 - 2}{-4-(-8)}=\frac{3}{-4 + 8}=\frac{3}{4} \). We can verify with other points, e.g., \((-4,5)\) and \((4,11)\): \( m=\frac{11 - 5}{4-(-4)}=\frac{6}{8}=\frac{3}{4} \), which is consistent.

Answer:

\(\frac{3}{4}\)