Unit Rates & Proportions
Find the unit rate:
84 miles in 12 days
7 miles per day or 7 miles/day
Use a graph to tell whether x and y are in a proportional relationship
x: 2 4 6 8
y: 10 20 30 40
Solve the proportion
x/8 = 9/4
x=18
Tell whether x and y show direct variation. Explain your reasoning.
xy-11=5
no; the equation cannot be written as y=kx.
Tell whether the rates form a proportion
1/9, 6/54
yes
Use a graph to tell whether x and y are in a proportional relationship
x: 1 3 5 7
y: 3 7 11 15
Solve the proportion
17/3 = y/6
y=34
Tell whether x and y show direct variation. Explain your reasoning.
x= 3/y
no; The equation cannot be written as y=kx
Tell whether the rates form a proportion
9/12, 8/72
no
Use the table to write a proportion
Monday Tuesday
Gallons 6 8
Miles 180 m
6 gallons/8 gallons = 180 miles/m or
6 gallons/180 miles = 8 gallons/m
Graph the line that passes through the two points. Then find the slope.
(15, 9) (-5, -3)
slope: 3/5
Tell whether x and y show direct variation. Explain your reasoning.
y/x = 8
yes; the equation can be written as y=kx
Find the unit rate:
2 2/5 kilometers in 3 3/4 minutes
16/25 kilometers per minute or 16/25 km/minute
Use the table to write a proportion
Thursday Friday
Classes 6 c
Hours 8 4
6 classes/8 hours = c/4 hours or
6 classes/c = 8 hours/4 hours
Graph the line that passes through the two points. Then find the slope.
(2, 9), (4, 18)
Slope: 9/2
Five movie tickets cost $36.25, what is the cost of 8 movie tickets?
$58
A specific shade of green glaze requires 5 parts blue to 3 parts yellow. A glaze mixture contains 25 quarts of blue and 9 quarts of yellow. How can you fix the mixture to make the specific shade of green glaze?
Add 6 quarts of yellow
These points when graphed shows the number of cycles of a crosswalk signal during the day and during the night. Graph these two lines and answer the following questions:
x=hours and y=cycles
Day: (2, 80) and (4, 160)
Night: (3, 90) and (5, 150)
a) Compare the steepness of the lines. What does this mean in the context of the problem?
b) Find and interpret the slope of each line
a) the number of cycles during the day is greater that the number of cycles during the night
b) Day: 40 Night: 30
The crosswalk cycles 40 times per hour during the day and 30 times per hour during the night.