Question

a line passes through the points in this table.

x	y
5	19
10	15
20	7
25	3

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 \((5, 19)\) and \((10, 15)\). Here, \( x_1 = 5 \), \( y_1 = 19 \), \( x_2 = 10 \), \( y_2 = 15 \).

Step3: Calculate slope

Substitute into the formula: \( m = \frac{15 - 19}{10 - 5} = \frac{-4}{5} \). We can verify with another pair, say \((10, 15)\) and \((20, 7)\): \( m = \frac{7 - 15}{20 - 10} = \frac{-8}{10} = \frac{-4}{5} \), which matches.

Answer:

\(-\frac{4}{5}\)