Question

the table represents a linear function.

x	y
-4	-2
-2	-10
-1	-14
1	-22
2	-26

what is the slope of the function?
-8
-4
2
5

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line passing through 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 from the table

Let's take the first two points \((-4, -2)\) and \((-2, -10)\). Here, \( x_1=-4 \), \( y_1 = -2 \), \( x_2=-2 \), \( y_2=-10 \).

Step3: Calculate the slope

Substitute the values into the slope formula:
\( m=\frac{-10 - (-2)}{-2 - (-4)}=\frac{-10 + 2}{-2 + 4}=\frac{-8}{2}=-4 \)

We can verify with another pair of points, say \((-2, -10)\) and \((-1, -14)\):
\( m=\frac{-14 - (-10)}{-1 - (-2)}=\frac{-14 + 10}{-1 + 2}=\frac{-4}{1}=-4 \)

Answer:

-4