Question

a line passes through the points in this table.
x | y
13 | 22
14 | 16
15 | 10
16 | 4
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 \((13, 22)\) and \((14, 16)\). Here, \( x_1 = 13 \), \( y_1 = 22 \), \( x_2 = 14 \), \( y_2 = 16 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{16 - 22}{14 - 13}=\frac{-6}{1}=-6 \). We can verify with other points (e.g., \((14,16)\) and \((15,10)\)): \( \frac{10 - 16}{15 - 14}=\frac{-6}{1}=-6 \), and \((15,10)\) and \((16,4)\): \( \frac{4 - 10}{16 - 15}=\frac{-6}{1}=-6 \), so the slope is consistent.

Answer:

\(-6\)