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 the values into the slope formula: \( m=\frac{23 - 31}{8 - 7}=\frac{-8}{1}=-8 \). We can verify with other points, for example, between \((8, 23)\) and \((9, 15)\): \( m=\frac{15 - 23}{9 - 8}=\frac{-8}{1}=-8 \), and between \((9, 15)\) and \((10, 7)\): \( m=\frac{7 - 15}{10 - 9}=\frac{-8}{1}=-8 \). So the slope is consistent.

Answer:

\(-8\)