Questions: Which two functions have the same rate of change? Select all that apply. A. y=4x-7 B. y=0.5x-1 C. n=0.6r+1 D. t=0.5n+1

Transcript text: Which two functions have the same rate of change? Select all that apply. A. $y=4 x-7$ B. $y=0.5 x-1$ C. $n=0.6 r+1$ D. $t=0.5 n+1$

Solution

Solution Steps

To determine which functions have the same rate of change, we need to identify the coefficients of the variable terms in each linear equation. The rate of change in a linear function is represented by the slope, which is the coefficient of the variable. We will compare these coefficients to find functions with the same rate of change.

Step 1: Identify the Functions and Their Slopes

We have the following functions and their corresponding slopes:

$ A: y = 4x - 7 $ has a slope of $ 4 $.
$ B: y = 0.5x - 1 $ has a slope of $ 0.5 $.
$ C: n = 0.6r + 1 $ has a slope of $ 0.6 $.
$ D: t = 0.5n + 1 $ has a slope of $ 0.5 $.

Step 2: Compare the Slopes

Next, we compare the slopes:

The slope of $ B $ is $ 0.5 $.
The slope of $ D $ is also $ 0.5 $.
The slopes of $ A $ and $ C $ are different from each other and from $ B $ and $ D $.

Step 3: Determine Functions with the Same Rate of Change

Since both $ B $ and $ D $ have the same slope of $ 0.5 $, they are the functions that share the same rate of change.