Compare linear function 1 with linear function 2. Which one has the greater rate of change?

Question

. Linear function 1: y=15x+8
. Linear function 2:
x= 5 and 13
y= 26 and 34.

Answer A: Linear function 1 has the greater rate of change, with a rate of change equal to 15 while Linear function 2 has a rate of change equal to 1.
Answer B: Linear function 2 has the greater rate of change, with a rate of change equal to 21 while linear function 1 has a rate of change equal to 9.
Answer C: Linear function 1 has the greater rate of change, with a rate of change equal to 8 while Linear function 2 has a rate of change equal to 1.
Answer D: Linear function 2 has the greater rate of change, with a rate of change equal to 21 while Linear function 1 has a rate of change equal to 15.

Explain your answer.

Answer 1

The rate of change of a linear function can be determined by the coefficient of x in the equation.

For Linear function 1, the equation is y = 15x + 8. The coefficient of x is 15, which means that for every increase in x by 1 unit, y increases by 15 units. Therefore, the rate of change for Linear function 1 is 15.

For Linear function 2, we are given two points (5, 26) and (13, 34). To find the rate of change, we need to find the change in y divided by the change in x.

The change in y is: 34 - 26 = 8
The change in x is: 13 - 5 = 8

Therefore, the rate of change for Linear function 2 is 8/8 = 1.

Comparing the rates of change, we can see that Linear function 1 has a greater rate of change (15) compared to Linear function 2 (1).

Therefore, the correct answer is A: Linear function 1 has the greater rate of change, with a rate of change equal to 15 while Linear function 2 has a rate of change equal to 1.