Vocabulary
What is the name of the point (0, 0)?
Origin
Write a variation equation for the following.
The amount of money you make varies directly with the number of magazines you sell.
m=kn
Write a variation equation for the following.
The volume of gas in a container varies inversely with the pressure.
v=k/p
The graph of a positive rate of change would have a positive ________________.
Slope
The constant of variation is typically represented by what letter?
k
Write a variation equation for the following.
The amount of time it takes you to complete your homework varies directly with how much you completed during class. The constant of variation is 12.
t=12c
Write a variation equation for the following.
The time is takes you to get to school varies inversely with your driving speed, and the constant of variation is 200.
t=200/s
Find the rate of change for the following:
x y
3 6
4 12
Rate of change:
6
What is the name of the graphs for inverse variation?
Hyperbola
Find the constant of variation for the following situation.
The cost of a pizza varies directly with the number of toppings. A pizza costs $12 when there are three toppings.
k=4
Find the constant of variation for the following situation.
The brightness of a light varies inversely with your distance from it. The brightness is 700 lumens when you are 6 feet from the light.
k=4,200
Find the rate of change for the following:
x y
5 10
9 6
Rate of change:
-1
For the following, identify which line is the x-axis and which line is the y-axis.
y=0
x=0
y=0 is the x-axis
x=0 is the y-axis
Write a variation equation for the following.
The weight of an object on Earth varies directly with its weight on the moon, and an object that weighs 360 pounds on Earth weighs 60 pounds on the moon.
e=60m
Write a variation equation for the following.
The amount of time it takes to complete a project varies inversely with the number of people working. Ten people working would make the project take 3 hours.
t=30/p
Is the following rate of change positive or negative. Describe what the graph would look like over this interval.
x y
3 6
4 8
- Positive
- Graph would be increasing
- Positive slope
Describe, in your own words, what rate of change is.
- Change in y divided by change in x
- Slope
- Change over time
Write a variation equation and solve the problem.
The distance required to stop a car varies directly with the car's speed. If a car going 50 mph takes 200 ft to stop, how long would it take a car going 80 mph to stop?
d=4s
320 ft.
Write a variation equation and solve the problem.
The current in an electrical circuit varies inversely to its resistance. If circuit's current is 80 amps when its resistance is 20 ohms, find its current when its resistance is 10 ohms.
c=1,600/r
160 amps
Is the following rate of change positive or negative. Describe what the graph would look like over this interval. Then give the rate of change.
x y
7 9
9 5
- Rate of Change: -2