Question

a line passes through the points in this table.

x	y
7	31
8	23
9	15
10	7

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 \((7, 31)\) and \((8, 23)\). Here, \( x_1 = 7 \), \( y_1 = 31 \), \( x_2 = 8 \), \( y_2 = 23 \).

Step3: Calculate the slope

Substitute into the formula: \( m = \frac{23 - 31}{8 - 7} = \frac{-8}{1} = -8 \). We can verify with other points (e.g., \((8,23)\) and \((9,15)\)): \( \frac{15 - 23}{9 - 8} = \frac{-8}{1} = -8 \), which confirms the slope.

Answer:

\(-8\)