Question

a line passes through the points in this table.

x	y
16	36
20	22
24	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

Let's take the first two points \((12, 50)\) and \((16, 36)\). Here, \( x_1 = 12 \), \( y_1 = 50 \), \( x_2 = 16 \), \( y_2 = 36 \).

Step3: Calculate the slope

Substitute into the formula: \( m=\frac{36 - 50}{16 - 12}=\frac{-14}{4}=-\frac{7}{2} \). We can verify with other points (e.g., \((16,36)\) and \((20,22)\)): \( \frac{22 - 36}{20 - 16}=\frac{-14}{4}=-\frac{7}{2} \), and \((20,22)\) and \((24,8)\): \( \frac{8 - 22}{24 - 20}=\frac{-14}{4}=-\frac{7}{2} \), so the slope is consistent.

Answer:

\(-\frac{7}{2}\)