Question

if a table shows ( x = 1, 2, 3 ) and ( y = 2.5, 5, 7.5 ), what is the slope of the function?

a. 4

b. 1.5

c. 2.5

d. 3

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). We can take two points from the given \( x \) and \( y \) values. Let's take \( (x_1,y_1)=(1, 2.5) \) and \( (x_2,y_2)=(2, 5) \).

Step2: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{5 - 2.5}{2 - 1}=\frac{2.5}{1} = 2.5 \). We can also check with another pair of points, say \( (2,5) \) and \( (3,7.5) \). Then \( m=\frac{7.5 - 5}{3 - 2}=\frac{2.5}{1}=2.5 \), which confirms the slope.

Answer:

c. 2.5