Compare Linear Function 1 with Linear Function 2. Which one has the lesser rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.
• Linear Function 1: y = 7х + 4
• Linear Function 2:
х У
10 61
12 73
To find the rate of change for each linear function, we need to compare the difference in y-values divided by the difference in x-values.
For Linear Function 1: y = 7x + 4
To find the rate of change, we can choose any two points from the function. Let's choose x = 10 and x = 12.
When x = 10, y = 7(10) + 4 = 74.
When x = 12, y = 7(12) + 4 = 88.
The difference in y-values is 88 - 74 = 14.
The difference in x-values is 12 - 10 = 2.
The rate of change for Linear Function 1 is 14/2 = 7.
For Linear Function 2: x, y
When x = 10, y = 61.
When x = 12, y = 73.
The difference in y-values is 73 - 61 = 12.
The difference in x-values is 12 - 10 = 2.
The rate of change for Linear Function 2 is 12/2 = 6.
Comparing the rates of change, we find that the rate of change for Linear Function 1 is 7, while the rate of change for Linear Function 2 is 6.
Therefore, Linear Function 1 has the greater rate of change.