Question

the table represents a linear function.

x	y
-2	-2
-1	1
0	4
1	7
2	10

what is the slope of the function?
options: 4, 3, -2, -3

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 from the table

Let's take the points \((-1, 1)\) and \((0, 4)\). Here, \( x_1=-1 \), \( y_1 = 1 \), \( x_2=0 \), \( y_2 = 4 \).

Step3: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{4 - 1}{0 - (-1)}=\frac{3}{1}=3 \). We can also check with other points, for example, \((0, 4)\) and \((1, 7)\): \( m=\frac{7 - 4}{1 - 0}=\frac{3}{1}=3 \), which confirms the slope.

Answer:

3