Question

a line passes through the points in this table.

x	y
2	5
3	2
4	-1
5	-4

what is the slope of the line?
write your answer as an integer or simplified fraction.

submit

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 \((2, 5)\) and \((3, 2)\). Here, \( x_1 = 2 \), \( y_1 = 5 \), \( x_2 = 3 \), \( y_2 = 2 \).

Step3: Calculate the slope

Substitute the values into the formula: \( m=\frac{2 - 5}{3 - 2}=\frac{-3}{1}=-3 \). We can verify with other points, e.g., \((3,2)\) and \((4, - 1)\): \( m=\frac{-1 - 2}{4 - 3}=\frac{-3}{1}=-3 \), and \((4,-1)\) and \((5, - 4)\): \( m=\frac{-4-(-1)}{5 - 4}=\frac{-3}{1}=-3 \). So the slope is consistent.

Answer:

\(-3\)