Question

Function 1: y = 4x + 5
Function 2: The line passing through the points (1, 6) and (3, 10).

Which of these functions has the greater rate of change?
A)
Function 1, because the slope is 5 and the slope of function 2 is 4.
B)
Function 1, because the slope is 4 and the slope of function 2 is 2.
C)
Function 2, because the slope is 7 and the slope of function 1 is 5.
D)
Function 2, because the slope is 5 and the slope of function 1 is 4.

Answer 1

y=mx+b is the general equation where m is the slope, so without even calculate the slope of function 2, only answer B is correct.
To calculate the slope, the equation is \[(y{2}-y {1})/(x{2}-x{1})\]
which is (10-6)/(3-1)

Answer 2

Rate of change (m) is:\[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]In A the slope is:\[m=\frac{ 9-13 }{ 1-2 }=\frac{ -4 }{ -1 }=4\]In B the slope is: \[m=\frac{ 6-10 }{ 1-3 }=\frac{ -4 }{ -2 }=2\] So the answer is B

Answer 3

Thanks so much!! B was the correct answer (: