Is It Proportional?
A table shows x: 1, 2, 3 and y: 5, 10, 15. Is the relationship proportional?
Yes. y is always 5 times x, so all the ratios are equivalent.
4 notebooks cost $12. What is the constant of proportionality for cost per notebook?
3 ($3 per notebook)
In the equation y = 6x, what is the constant of proportionality?
6
The graph of every proportional relationship is a straight line that passes through what point?
The origin, (0,0)
Leo earns $11 per hour. He works 3 hours on Saturday and 5 hours on Sunday. How much does he earn in all?
$88
Every rectangle in a set is 3 cm longer than it is wide. Are length and width proportional?
No. You add 3 instead of multiplying by a constant (a 1×4 and a 2×5 rectangle don't have equivalent ratios).
Hours: 2, 4, 6. Miles: 14, 28, 42. What is the constant for miles per hour?
7
Movie tickets cost $9 each. Write an equation for the total cost, c, of t tickets.
c = 9t
A graph shows pounds of grapes (x) and cost (y). It passes through (1, 2.5). What does that point mean?
1 pound of grapes costs $2.50. That's the unit rate, or constant of proportionality.
Two friends are 40 miles apart and bike toward each other. They meet after 2 hours. One rides at 12 mph. How fast does the other ride?
8 mph. The first friend rides 24 miles, so the other rides 16 miles in 2 hours.
People: 2, 4, 5. Pizza slices: 6, 12, 16. Proportional?
No. 6 ÷ 2 = 3 and 12 ÷ 4 = 3, but 16 ÷ 5 = 3.2.
Dani swims 9 laps in 1/3 of an hour. What is the constant of proportionality for laps per hour?
27 laps per hour
Jada uses c = 12h to find what she charges for h hours of babysitting. She charges $54. How many hours did she babysit?
4.5 hours
A proportional graph passes through (4, 10). What is the constant of proportionality, and what is the equation?
k = 2.5, so y = 2.5x
A recipe makes 6 cups of lemonade with 1/2 cup of sugar. Ana has 1 cup of sugar. Can she make 15 cups? If not, how much more sugar does she need?
No. She needs 1 1/4 cups, so she's 1/4 cup short.
A double number line shows gallons of paint (1/2, 1, 1 1/2, 2) and square feet covered (150, 300, 450, 600). Is the relationship proportional?
Yes. Every ratio equals 300 square feet per gallon, so square feet is always 300 times the gallons.
A recipe uses 3/4 cup of flour for every 1/2 cup of sugar. What is the constant for cups of flour per cup of sugar?
3/2, or 1.5
Plant food directions say 1 teaspoon for every 3 cups of water. Write an equation for teaspoons of plant food, f, in w cups of water.
f = (1/3)w
A graph of minutes reading (x) and pages read (y) is proportional and passes through (6, 9). How many pages are read in 10 minutes?
15 pages (k = 1.5)
Store A sells 5 shirts for $40. Store B sells 3 shirts for $27. How much do you save buying 15 shirts at the cheaper store?
$15. Store A charges $120 and Store B charges $135.
A gym charges a $25 sign-up fee plus $10 per month. Is total cost proportional to the number of months? Explain.
No. 1 month costs $35 and 2 months cost $45, and those ratios aren't equivalent. Also, 0 months would cost $25, not $0.
5 pounds of apples cost $8. Give BOTH constants of proportionality: dollars per pound AND pounds per dollar.
$1.60 per pound, and 5/8 (0.625) pound per dollar
Do y = 4x and x = (1/4)y represent the same proportional relationship? Explain.
Yes. They describe the same pairs of values, just with the variables switched. For example, (2, 8) works in both. The constants are reciprocals because each one compares the quantities in the opposite order.
A proportional line passes through (3, 2). Marco says the equation is y = (3/2)x. Find his mistake and give the correct equation.
He divided x by y instead of y by x. The correct constant is 2 ÷ 3 = 2/3, so y = (2/3)x.
A club has 63 students. The ratio of boys to girls is 3 : 4. How many more girls than boys are in the club?
9 more girls (27 boys, 36 girls)