Question

the table represents a linear function.

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

what is the slope of the function?

• -10
• -5
• 5
• 10

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 points \((0, 4)\) and \((2, 14)\). Here, \( x_1 = 0 \), \( y_1 = 4 \), \( x_2 = 2 \), \( y_2 = 14 \).

Step3: Calculate the slope

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

Answer:

5