Ratios and Rates
Write the ratio as a fraction in simplest form.
25 to 45
5/9
Tell whether the ratios form a proportion.
1/3 and 7/21
Yes
Use the table to write a proportion.
Game 1: 12 points in 14 shots
Game 2: 18 points in "x" shots
12/14 = 18/x
What is slope?
Slope is the rise over the run.
Slope is your change in y-values over your change in x-values.
What is direct variation?
Direct variation is when two quantities show a relation through the constant of proportionality (k) and passes through the origin.
Find the unit rate.
180 miles in 3 hours
60 miles per hour
Tell whether x and y are proportional.
x: 1 2 3 4
y: 7 8 9 10
No
Solve the proportion.
1/4 = x/20
x=5
Find the slope of the line with the following points.
(0,0) and (1,4)
Slope = (4-0) / (1-0) = 4/1 = 4
p.202 #6
Yes, the line passes through the origin. k=2
Use the ratio table to find the unit rate with the specified units.
Servings per Package
Packages: 3 6 9
Servings: 13.5 27 40.5
4.5 servings per package
Tell whether the two rates form a proportion.
7 inches in 9 hours; 42 inches in 54 hours
Yes
Use the table to write and solve a proportion.
May: "x" winners in 85 entries
June: 34 winners in 170 entries
x/85 = 34/170
x=17 winners
Find the slope of the line with the following points.
(3,2) and (6,3)
Slope = (3-2) / (6-3) = 1/3
p.202 #8
No, the line does not pass through the origin.
Are the two statements equivalent? Explain your reasoning.
The ratio of boys to girls is 2 to 3.
The ratio of girls to boys is 3 to 2.
Yes, they are the inverse of one another. Both are boys to girls of 2 to 3.
Tell whether the two rates form a proportion. Explain.
68 hits in 172 at bats; 43 hits in 123 at bats
No, they do not have equivalent ratios.
Solve the proportion.
1.4/2.5 = x/25
x=14
Graph the data. Then find and interpret the slope of the line through the points.
p.196 #10
See graph.
Slope = 45 words / minute
You type 45 words every minute.
p.202 #10
No, the equation cannot be written as y=kx and will not pass through the origin.
You mix 1/4 cup of juice for every 2 cups of water to make 18 cups of mixed juiced water. How much juice and water do you use?
2 cups of juice and 16 cups of water
You can do 90 sit-ups in 2 minutes. Your friend can do 135 sit-ups in 3 minutes. Do these rates form a proportion? Explain.
Yes, they both do 45 sit-ups per minute.
Write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
6 km = "x" mi
(1 km = 0.621371 mi)
x=3.73 mi
What is the slope of a line that passes through the points (2,0) and (5,0)? Explain.
Slope = (0-0) / (5-2) = 0/3 = 0
p.202 #11
Yes, the equation can be written as y=kx; k=5/2. And it passes through the origin.