Direct Variation
This Equation describes a relationship where y varies directly with x, and y=12 when x=4
What is
y=3x
This is the general equation that represents an inverse variation between x and y
What is y=k/x
A car’s distance traveled varies directly with time. If it travels 120 miles in 2 hours, how far will it go in 5 hours?
What is 300 miles?
if y =3x, this is the value of y when x = 10
What is 30?
if y=k/x and y=4 when x=3, this is the value of k
What is 12?
The time it takes to complete a job varies inversely with the number of workers. If 4 workers can do it in 6 hours, how long would it take 8 workers?
What is 3 hours?
if y varies directly with x and y =20 when x =5, this is the value of x when y= 32.
What is 8?
if y varies inversely with x, and y =6 when x=2, what is the value of y when x =4
what is 3?
The brightness of a light varies inversely with the square of the distance from the source. If brightness is 100 at 2 meters, what is it at 4 meters?
What is 25?
This is how you know a relationship between x and y is a direct variation
The ratio is constant so it would cross the point (0,0) in a graph and is a straight line
How can you tell if a relationship is an inverse variation
What is the product xy is constant or the equation y=k/x can be used to represent it
The amount of money earned varies directly with the number of hours worked. If someone earns $90 in 6 hours, how much will they earn in 10 hours?
What is $150?
Given this table, is the relationship a direct variation?_
x | y
2 , 6
4 , 12
6 , 18
What is Yes, it's a direct variation as y/x =3 every time?
Using this table, see if it shows an inverse variation
x | y
2 , 12
3 , 8
4 , 6
What is
yes, the product xy is 24 for all pairs.
A planet’s gravitational force varies inversely with the square of the distance from its center. If the force is 36 N at 2 units away, what is the force at 6 units?
What is 4 N?