Question

a line passes through the points in this table.

x | y
4 | 9
12 | -9
20 | -27
28 | -45

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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Choose two points

Let's take the first two points \( (4, 9) \) and \( (12, -9) \). Here, \( x_1 = 4 \), \( y_1 = 9 \), \( x_2 = 12 \), \( y_2 = -9 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{-9 - 9}{12 - 4}=\frac{-18}{8}=\frac{-9}{4} \). We can verify with other points, e.g., \( (12, -9) \) and \( (20, -27) \): \( \frac{-27 - (-9)}{20 - 12}=\frac{-18}{8}=\frac{-9}{4} \), which matches.

Answer:

\( -\frac{9}{4} \)