Proportional Relationships
What does it mean for two quantities to be proportional?
Their ratios are equivalent, and the graph is a straight line through the origin.
What is the constant of proportionality?
The unit rate (k) that relates two proportional quantities.
Compute the unit rate: ½ mile in ¼ hour
2 miles per hour
What must be true for two drawings to be scale drawings of each other?
All side lengths must be proportional
Write a ratio of 8 boys to 12 girls in simplest form.
2:3
A boy sends 5 texts for every 7 texts a girl sends. Is this a proportional relationship?
Yes, because the ratios are consistent and graph as a straight line through the origin
A song earns a singer $1 for every $5 the store makes. Write the equation.
y=1/5x
A bike shop discounts bikes by ⅓. If the bike costs $327, what’s the discount?
$109
If the scale is 1 inch = 5 feet, how long is a 3-inch drawing in real life?
15 feet
If a recipe calls for 3 cups of flour to 4 cups of sugar, how much flour for 8 cups of sugar?
6 cups of flour
Josiah earns $14/hr and Tillery earns $7/hr, but both get a $2/hr raise each year. Is their pay proportional?
No, because the increase is not multiplicative; the ratios are not constant
On a graph of a proportional relationship, what does the point (1, r) represent?
The unit rate (constant of proportionality) .
A music player is marked down ¼ to $128. What was the original price?
$170.67 (approx)
What is the constant of proportionality in a scale drawing?
The scale factor
A car uses 6 gallons of gas after 120 miles. What’s the unit rate in mpg?
20 miles per gallon
If a table of values shows different unit rates for the same quantities, what does that mean?
The relationship is not proportional.
A store sells 3 books for $15. What is the constant of proportionality in dollars per book?
$5 per book
If blackberries and juice form a proportional relationship, how do you find the equation?
Find the constant of proportionality (cups of juice per cup of berries) and write y=kx.
A floor plan has a bedroom that measures 2 inches by 3 inches. If the scale is 1 in = 4 ft, what are the real dimensions?
8 ft by 12 ft.
A scale drawing uses 1 cm = 0.5 m. What is the real length of a 12 cm line?
6 meters
Explain what the point (0,0) means on a proportional graph
It means zero of one quantity results in zero of the other .
How can you tell from a graph if a relationship is proportional?
The graph is a straight line through the origin
A music player is marked down ¼ to $128. What was the original price?
$170.67
What happens if only one pair of sides is proportional but others are not?
The image is not a scale drawing.