​Prove that the linear function f(x)=3x−7
changes by equal amounts over equal intervals of length 5
.

Step 1: Choose two input values for x
. Let's use s
and s+5
. We use the two values of x
where the difference between them is 5
.

Step 2: Let's solve for the output values f(s)
and f(s+5)
. The first one is found for you. Find the other value.

f(s)=3s−7
Type your answer in the box.

f(s+5)=3(s+5)−7 =
Question 2
Step 3: Let's find the difference between the two output values f(s+5)
and f(s)
. This way we can determine how much the output values change between the two inputs.

Type your answer in the box.

f(s+5)−f(s) =

Question 3
Step 4: Let's generalize the result. What does the difference you found in the previous step tell you?

Use the drop-down arrows to complete the sentences.

The function f(x)=3x −7
is
linear
. We know this because over intervals of 3
for x
-values, the difference of the corresponding function values is
not constant
.