Tables & Double Number Lines
A double number line shows batches (0, 1, 2, 3) over cups of flour (0, 3, 6, 9). How much flour is needed for 5 batches?
15 cups
Each movie ticket costs $6. What is the constant of proportionality for cost per ticket?
6
A graph is a straight line that starts at (0, 3). Is it a proportional relationship?
No. It doesn’t pass through the origin.
Jada earns $12 per hour. She works 4 hours on Monday and 3 hours on Tuesday. How much does she earn?
$84
Mason says 2 : 3 is equivalent to 4 : 5 because he added 2 to both numbers. What’s wrong?
You multiply to make equivalent ratios, not add. 2 : 3 is equivalent to 4 : 6.
A table shows dogs: 1, 2, __, 5 and treats: 4, 8, 12, __. Fill in both missing values.
3 dogs, 20 treats
Hours: 2, 3, 5. Pay: $30, $45, $75. Is this relationship proportional? If so, what is the constant?
Yes. The constant is 15 ($15 per hour).
A proportional graph passes through (1, 7). What is its equation?
y = 7x
Two friends are 18 miles apart and walk toward each other. They meet after 2 hours. One walks 4 mph. How fast does the other walk?
5 mph. The first friend walks 8 miles, so the other walks 10 miles in 2 hours.
Zoe says the ages of two sisters are proportional, because when the younger sister is 4 the older one is 7, and when the younger sister is 8 the older one is 11. What’s wrong?
The older sister is always 3 years older, so you add 3 instead of multiplying. The ratios 4 : 7 and 8 : 11 aren’t equivalent, so the ages aren’t proportional.
A double number line shows minutes (0, 1, 2, 3) over pages read (0, 2.5, 5, 7.5). How many pages are read in 10 minutes?
25 pages
3 pounds of rice cost $4.50. Write an equation for the cost, c, of p pounds.
c = 1.5p
A graph shows gallons of gas (x) and miles driven (y). It passes through (3, 75). What does that point mean, and what is the constant of proportionality?
The car goes 75 miles on 3 gallons, so the constant is 25 miles per gallon.
A trail mix recipe makes 5 cups using 1/2 cup of chocolate chips. Leo has 1 cup of chips. Is that enough to make 12 cups of trail mix? If not, how much more does he need?
No. He needs 1.2 cups, so he is 0.2 (1/5) cup short.
A proportional graph passes through (5, 2). Leo says the constant of proportionality is 5/2. What’s wrong?
He divided x by y. The constant is y ÷ x = 2/5.
People: 3, 6, 9. Pizza slices: 8, 16, 24. What is the constant of proportionality for slices per person?
8/3, or 2 2/3 slices per person
x: 2, 4, 6.
y: 5, 10, 16.
Is the relationship proportional? If not, which value breaks the pattern?
No. The y-value 16 breaks it, because it should be 15 to keep the ratio at 2.5.
A proportional line passes through (4, 6). Is the point (10, 15) also on the line? Explain.
Yes. The constant is 1.5, and 1.5 × 10 = 15.
Store A sells 4 notebooks for $10. Store B sells 6 notebooks for $13.80. How much do you save buying 12 notebooks at the cheaper store?
$2.40. Store A charges $30.00 and Store B charges $27.60.
6 notebooks cost $9. Ava says 10 notebooks cost $13 because she added 4 to both numbers. Find the correct cost.
$15. Each notebook costs $1.50, and 10 × 1.50 = 15.
1/3 gallon of paint covers 120 square feet. Find BOTH constants: square feet per gallon and gallons per square foot.
360 square feet per gallon, and 1/360 gallon per square foot
A recipe uses 5 cups of flour for every 2 cups of sugar. Give BOTH constants of proportionality and say what each one means.
2.5 cups of flour per cup of sugar, and 0.4 (2/5) cup of sugar per cup of flour
Line A passes through the origin and (2, 8). Line B passes through the origin and (3, 9). Find each constant of proportionality. Which line is steeper?
Line A has a constant of 4 and Line B has a constant of 3, so Line A is steeper.
An animal shelter has 84 cats and dogs. The ratio of cats to dogs is 2 : 5. How many more dogs than cats are there?
36 more dogs (24 cats, 60 dogs)
A recipe makes 4 cups of punch with 2/3 cup of sugar. Kai says 10 cups of punch need 2/3 × 10 = 6 2/3 cups of sugar. Find his mistake and the correct answer.
He treated 2/3 cup as the amount per 1 cup of punch, but it’s for 4 cups. The rate is 1/6 cup per cup, so 10 cups need 1 2/3 cups of sugar.