Question

a line passes through the points in this table.

x	y
6	1
18	3
24	4
30	5

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 \((6, 1)\) and \((18, 3)\). Here, \( x_1 = 6 \), \( y_1 = 1 \), \( x_2 = 18 \), \( y_2 = 3 \).

Step3: Calculate the slope

Substitute into the formula: \( m=\frac{3 - 1}{18 - 6}=\frac{2}{12}=\frac{1}{6} \). We can verify with other points, e.g., \((24, 4)\) and \((30, 5)\): \( m=\frac{5 - 4}{30 - 24}=\frac{1}{6} \), which is consistent.

Answer:

\(\frac{1}{6}\)