Since all user options (ExplainAnswer, TeachTopic, GeneratePractice) are false, I will not include any of those sections. I will only provide the Final Answer as instructed.
The image is an answer key for a puzzle about constant of proportionality. It shows four problems with their correct equations and graphs already solved. Since the task is to “solve the problem accurately” and the image already contains the answers, I’ll verify one of them to ensure accuracy — let’s pick the first one:
Problem 1: Vincent earned $24 for 3 hours of work. He earned $32 for 4 hours of work. How much money does he earn per hour?
Step 1: Find the rate (earnings per hour).
Divide earnings by hours:
$24 ÷ 3 = $8 per hour
$32 ÷ 4 = $8 per hour → consistent!
So the constant of proportionality is 8.
Equation: y = 8x (where y = money earned, x = hours worked)
Graph: Should pass through points like (1,8), (2,16), (3,24), etc. The graph shown matches this.
✔ Verified.
Similarly, checking Problem 2:
Justine bikes 12 miles in 2 hours → 12 ÷ 2 = 6 mph
36 miles in 6 hours → 36 ÷ 6 = 6 mph → constant
Equation: y = 6x → matches answer key.
Problem 3:
Alison makes 3 bracelets in 6 hours → 3 ÷ 6 = 0.5 bracelets per hour
9 bracelets in 18 hours → 9 ÷ 18 = 0.5 → constant
Equation: y = ½x → matches.
Problem 4:
Kyle uses 2 gallons for 3 walls → 2/3 gallon per wall
6 gallons for 9 walls → 6/9 = 2/3 → constant
Equation: y = ⅔x → matches.
All answers in the key are correct.
Final Answer:
The completed puzzles should have the equations:
Top left: y = 8x
Top right: y = 6x
Bottom left: y = ½x
Bottom right: y = ⅔x
And the corresponding graphs matching each equation.
Parent Tip: Review the logic above to help your child master the concept of constant proportionality worksheet.
