Equations
Does the following equation have direct variation?
y=x
Yes!
The equation y=x has direct variation. The y-values vary directly with the x-values.
Does the description have direct variation?
A straight line that goes through the origin.
Yes!
A straight line that goes through the origin has direct variation!
Does the table with the following points have direct variation?
(-5, 10)
( 0, 0 )
( 5, -10)
The table has direct variation!
(-5, 10)
( 0, 0 )
( 5, -10)
Does the following problem have direct variation?
For a sports camp, a coach bought volleyballs for $9.95 each.
Yes! The problem has direct variation!
(For a sports camp, a coach bought volleyballs for $9.95 each.)
How many bakers does it take to bake a pi? (This is a math joke!)
3.14! (when rounded)
It takes 3.1415926... bakers to bake a pi! Ha! It's a funny joke!
Is the following equation proportional or non-proportional? y=-x
Proportional!
y=-x is proportional!
Does the description have direct variation?
A straight line that has a y-intercept of 0.5.
No!
A straight line with a y-intercept of 0.5 does not have direct variation!
Is the table with the following points proportional or non-proportional?
(-1, -5)
( 0, -4)
( 1, -3)
Non-proportional!
(-1, -5)
( 0, -4)
( 1, -3)
Does the following problem have direct variation?
A candy store had a sale on Laffy Taffy candy for $0.08 each if you bought a "Candy Pass" for $0.75.
No!
The following problem does not have a relationship with direct variation! (A candy store had a sale on Laffy Taffy candy for $0.08 each if you bought a "Candy Pass" for $0.75.)
Does the description have direct variation?
A wavy line that goes through the origin.
No!
A wavy line that goes through the origin does not have direct variation!
Does the following equation have direct variation? y=(5/3)x
Yes!
y=(5/3)x has direct variation!
Does the following graph have direct variation?
A straight line on a graph with y values that vary directly with x values.
Yes!
A straight line on a graph with y values that vary directly with x values has direct variation!
Does the table have direct variation?
( 2, 0.5)
( 4, 1.5)
( 6, 2.5)
No! The table does not have direct variation!
( 2, 0.5)
( 4, 1.5)
( 6, 2.5)
Is the following problem proportional or non-proportional?
A library charged a person $0.25 for every day a book was late plus a late fee of $1.00.
Non-proportional!
(A library charged a person $0.25 for every day a book was late plus a late fee of $1.00.)
Who is the best teaching intern in 8th grade math classes?
Ms. Carpenter!
Is the following equation proportional or non-proportional? y=9
Non-proportional!
y=9 is non-proportional!
Is the description proportional or non-proportional?
A straight line with the points (-1,5) and (0,0).
Proportional!
A straight line with the points (-1,5) and (0,0) is proportional!
Does the table of the following points have direct variation?
(-75, -6375)
(-74, -6290)
(-73, -6205)
Yes! The table has direct variation!
(-75, -6375)
(-74, -6290)
(-73, -6205)
You are buying apples for your teachers. The cost of apples is directly proportional to the number of apple purchased. If 9 apples cost $7.38, how much would it cost for you to buy 8 apples for all your teachers?
$6.56!
It will cost $6.56 to buy 8 apples if 9 apples cost $7.38!
What is the constant of variation in the following equation?
y=(-2/3)x
(-2/3)!
The constant of variation in
y=(-2/3)x is (-2/3)!
Is the following equation proportional or non-proportional? y=x3
Non-proportional!
y=x3 is non-proportional!
What is the constant of variation given by the following points?
(9, 4.5) and (10, 5)
0.5! (a.k.a. 1/2)!
The constant of variation for the points (9, 4.5) and (10, 5) is 0.5!
What is the y-intercept given by the points (3, 4.4) and (5, 6)?
2!
The y-intercept given by the points (3, 4.4) and (5, 6) is 2!
You are selling cookies in a bake sale. The money earned from selling cookies varies directly with the number of cookies sold. When 5 cookies are sold, you earn $6.25. How many cookies did you sell if you earned a total of $35.00?
28 cookies!
You sold 28 cookies to earn a total of $35.00 if you earned $6.25 from selling 5 cookies.
The total cost for tickets to the dance varies directly to the number of tickets purchased. If 5 tickets cost $15, identify the constant of variation and write an equation to represent the relationship.
constant of variation=$3/ticket
y=3x is the equation
(This is true if 5 tickets cost $15.)