Question

the table represents a linear function.
what is the slope of the function?

x	y
-4	-16
-2	-6
0	4
2	14
4	24

options: -10, -5, 5, 10

Explanation:

Step1: Recall slope formula

The slope \( m \) of a linear function 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 points \((-2, -6)\) and \((0, 4)\). Here, \( x_1=-2 \), \( y_1 = -6 \), \( x_2 = 0 \), \( y_2=4 \).

Step3: Calculate the slope

Substitute into the slope formula: \( m=\frac{4 - (-6)}{0 - (-2)}=\frac{4 + 6}{0 + 2}=\frac{10}{2}=5 \). We can also check with other points, for example, \((0,4)\) and \((2,14)\): \( m=\frac{14 - 4}{2 - 0}=\frac{10}{2}=5 \), which confirms the slope.

Answer:

5