Final Answer:
Problem 1: Function A has greater rate of change (5 > 3)
Problem 2: Function D has greater rate of change (2 > 1)
Problem 3: Function F has greater rate of change (3 > 1)
Problem 4: Function H has greater rate of change (2 > 1/3)
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Explanation:
Let’s go problem by problem so you can see how it works.
🔹 Problem 1:
Function A is y = 5x + 3 → This is easy! The number in front of x is the rate of change → that’s 5.
Function B has a table:
From x=1 to x=2, y goes from 6 to 9 → that’s +3.
From x=2 to x=3, y goes from 9 to 12 → that’s also +3.
So every time x goes up 1, y goes up 3 → rate of change = 3.
Compare: 5 vs 3 → 5 is bigger → Function A wins!
🔹 Problem 2:
Function C has a table:
x=2 to x=3 → y=9 to 10 → +1
x=3 to x=4 → y=10 to 11 → +1
So rate of change = 1.
Function D is a graph. Pick two points: say (0,2) and (2,6).
When x goes up 2, y goes up 4 → so rate of change = 4 ÷ 2 = 2.
Compare: 1 vs 2 → 2 is bigger → Function D wins!
🔹 Problem 3:
Function E is y = x – 2 → number in front of x is 1 → rate of change = 1.
Function F is a graph. Pick two points: say (3,0) and (5,6).
x goes up 2, y goes up 6 → rate of change = 6 ÷ 2 = 3.
Compare: 1 vs 3 → 3 is bigger → Function F wins!
🔹 Problem 4:
Function G has a table:
x=12 to x=18 → y=2 to 4 → x up 6, y up 2 → rate = 2 ÷ 6 = 1/3
x=18 to x=24 → y=4 to 6 → x up 6, y up 2 → same → 1/3
Function H is a graph. Pick (0,8) and (2,12).
x up 2, y up 4 → rate = 4 ÷ 2 = 2.
Compare: 1/3 vs 2 → 2 is bigger → Function H wins!
You’re just comparing how fast y grows when x grows — that’s what “rate of change” means!
Parent Tip: Review the logic above to help your child master the concept of comparing linear equations worksheet.
