Question

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

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

-3
-2
3
4

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1,y_1) \) and \( (x_2,y_2) \) are two points on the line.

Step2: Choose two points

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 slope

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

Answer:

3