Question

a line passes through the points in this table.

x	y
6	-7
10	-35
14	-63
18	-91

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 \((6, -7)\) and \((10, -35)\). Here, \( x_1 = 6 \), \( y_1=-7 \), \( x_2 = 10 \), \( y_2=-35 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{-35 - (-7)}{10 - 6}=\frac{-35 + 7}{4}=\frac{-28}{4}=-7 \). We can verify with other points (e.g., \((10, -35)\) and \((14, -63)\)): \( m=\frac{-63 - (-35)}{14 - 10}=\frac{-28}{4}=-7 \), which is consistent.

Answer:

\(-7\)