Question

Two linear functions are shown below which function has the greater rate of change

Answer 1

Answer:

On this case if we analyze both slopes, we see that function 2 has a greater rate of change because have a slope greater on absolute value than the slope for Function 1 (|-5|>|4|). No matter if the sign is positive or no we are analyzing the rate of change and for this case we need to use the absolute value to find the solution.

Step-by-step explanation:

Assuming the following two functions:

Function 1: y = 4x + 8

Function 2:  

x y

2 20

4 10

6 0

We can find the slope for the second function like this:

$m =\frac{10-20}{4-2}=-5$

And in order to find the intercept we can use any point for example (2,20) and we got:

$20 =-5(2) +b$

And then $b=30$

So our function 2 is given by: $y =-5x +30$

On this case if we analyze both slopes, we see that function 2 has a greater rate of change because have a slope greater on absolute value than the slope for Function 1 (|-5|>|4|). No matter if the sign is positive or no we are analyzing the rate of change and for this case we need to use the absolute value to find the solution.