Question

a line passes through the points in this table.

x | y
3 | 20
7 | 16
11 | 12
15 | 8

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 from the table

Let's take the first two points \((3, 20)\) and \((7, 16)\). Here, \( x_1 = 3 \), \( y_1 = 20 \), \( x_2 = 7 \), \( y_2 = 16 \).

Step3: Calculate the slope

Substitute the values into the slope formula: \( m = \frac{16 - 20}{7 - 3} = \frac{-4}{4} = -1 \). We can verify with other points (e.g., \((7,16)\) and \((11,12)\)): \( \frac{12 - 16}{11 - 7} = \frac{-4}{4} = -1 \), or \((11,12)\) and \((15,8)\): \( \frac{8 - 12}{15 - 11} = \frac{-4}{4} = -1 \), so the slope is consistent.

Answer:

\(-1\)