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

Let's take the first two points \((6, 41)\) and \((7, 31)\). Here, \( x_1 = 6 \), \( y_1 = 41 \), \( x_2 = 7 \), \( y_2 = 31 \).

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 is consistent.

Answer:

\(-10\)