Question

a line passes through the points in this table.

x	y
8	6
16	20
24	34

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 \((0, -8)\) and \((8, 6)\). Here, \( x_1 = 0 \), \( y_1=-8 \), \( x_2 = 8 \), \( y_2 = 6 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{6 - (-8)}{8 - 0}=\frac{6 + 8}{8}=\frac{14}{8}=\frac{7}{4} \). We can verify with other points (e.g., \((8,6)\) and \((16,20)\)): \( \frac{20 - 6}{16 - 8}=\frac{14}{8}=\frac{7}{4} \), which is consistent.

Answer:

\(\frac{7}{4}\)