Question

a line passes through the points in this table.

x	y
6	5
9	3
12	1

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 \((0, 9)\) and \((6, 5)\). Here, \( x_1 = 0 \), \( y_1 = 9 \), \( x_2 = 6 \), \( y_2 = 5 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{5 - 9}{6 - 0}=\frac{-4}{6}=\frac{-2}{3} \). We can verify with other points, e.g., \((6,5)\) and \((9,3)\): \( m=\frac{3 - 5}{9 - 6}=\frac{-2}{3} \), or \((9,3)\) and \((12,1)\): \( m=\frac{1 - 3}{12 - 9}=\frac{-2}{3} \).

Answer:

\(-\frac{2}{3}\)