November 12, 2012
At a local restaurant, 4 hamburgers can be
made from 1 pound of ground beef.
5.6
Direct Variation
I can identify, write, and graph a direct
variation.
At a local restaurant, 4 hamburgers can be
made from 1 pound of ground beef.
Pounds of
ground beef (x)
1
2
3
4
Hamburgers (y)
4
8
12
16
The equation y = 4x describes the
relationship...the number of
hamburgers varies directly with
the amount of ground beef.
Tell if the equation is a direct variation. If
it is, identify the constant of variation.
y = 2x
y=x+2
Direct variation?
Direct variation?
Constant of variation:
Constant of variation:
y = 2x - 3
½x + 0 = y
Direct variation?
Direct variation?
Constant of variation:
Constant of variation:
Pounds of
ground beef (x)
1
Hamburgers (y)
4
2
3
4
What is the rate of change??
Direct variation:
-special linear relationship
-written in the form y = kx
"constant of variation"
(can't be 0)
*no number being added or subtracted,
so (0, 0) is always on the graph!!!
Tell if the equation is a direct variation. If
it is, identify the constant of variation.
*Hint: What do you need to do first??
-3x + 5y = 0
2x + y = 10
Direct variation?
Direct variation?
Constant of variation:
Constant of variation:
November 12, 2012
Think back to the hamburger example...
Pounds of
ground beef (x)
1
2
3
4
Hamburgers (y)
4
8
12
16
Pounds of
ground beef (x)
1
2
3
4
Hamburgers (y)
4
8
12
16
Equation: ____________
Direct Variation MUST have (0, 0) on the graph.
Constant of Variation: __________
Find the slope between (1, 4) and (0, 0)
*What would the
graph look like??
Find the slope between (3, 12) and (0, 0)
*What is always the same?
What do you notice??
To determine if a relationship shows
DIRECT Variation (tomorrow we'll talk about
other types of variation)
you find the slope between a point and (0, 0)
Tell if the table shows a direct variation. If
it does, identify the constant of variation.
y=kx... so k=
In other words….
take the y-value divided by the x-value!
Algebraically….
y = kx so … k =
Direct variation?
Direct variation?
Constant of variation:
Constant of variation:
The ordered pair (7, 21) is the solution of a
direct variation. Write the equation for the
direct variation. Graph the equation.
The value of y varies directly with x, and
y = 6 when x = 12. Find y when x = 18.
y = kx
Find the value of k.
Write the equation.
Solve for the missing variable.
y = kx
November 12, 2012
The value of y varies directly with x,
and y = 9 when x = 3.
Find y when x =⅔.
y = kx
Find the value of k.
You
!
tr y
Write the equation.
Solve for the missing variable.