Question

a line passes through the points in this table.

x	y
6	41
7	31
8	21
9	11

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: \( (x_1, y_1)=(6, 41) \) and \( (x_2, y_2)=(7, 31) \).

Step3: Calculate the slope

Substitute into the formula: \( m=\frac{31 - 41}{7 - 6}=\frac{- 10}{1}=-10 \). We can verify with other points (e.g., \( (7,31) \) and \( (8,21) \)): \( \frac{21 - 31}{8 - 7}=\frac{-10}{1}=-10 \), which confirms the slope.

Answer:

\(-10\)