Answer:
Function A has a rate of change of -5 and Function B has a rate of change of -4.5, so Function B has a greater rate of
Step-by-step explanation:
Function A:
[tex]\begin{array}{cccccc}x & {1.5} & {2.5} & {3.5} & {4.5} & {5.5} \ \\ y & {5} & {0} & {-5} & {-10} & {-15} \ \end{array}[/tex]
Function B:
[tex]y = -4.5x + 15[/tex]
Required
Which has a greater rate of change
The rate of change of function A is calculated as thus:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex](x_1,y_1) = (1.5,5)[/tex]
[tex](x_2,y_2) = (2.5,0)[/tex]
So, we have:
[tex]m = \frac{0-5}{2.5 - 1.5}[/tex]
[tex]m = \frac{-5}{1}[/tex]
[tex]m = -5[/tex]
For function B
The general function is:
[tex]y = mx + b[/tex]
Where
m is the rate of change
By comparing [tex]y = mx + b[/tex] to [tex]y = -4.5x + 15[/tex]
[tex]m = -4.5[/tex]
So, we have that:
Function A has a rate of -5; function B has a rate of -4.5.
By comparison: -4.5 is greater than 5
Hence, function B has a greater rate.
