November 13, 2015
5.5 Direct Variation
direct variation y varies directly with x
any function that can be written in the form y = k x, where k is
the coefficient of x and k = 0
notice: the function is a monomial with a
degree of 1
this is a proportional relationship, where K is the scale factor
constant of variation the coefficient of x in a direct variation; 'k', the scale factor
of a proportional relationship
November 13, 2015
November 13, 2015
An equation is a direct variation if:
•
its graph is a line that passes through zero, or
•
the equation can be written in the form y = kx.
• the table has a y value of zero when the x value is
zero and y increases proportionally with x
November 13, 2015
k=-7
k=3
k=1/2
5x + 2y = 0
Solve for y.
1. Subtract 5x.
2. Divide by 2.
Yes, it’s a direct variation.
Constant of variable, k, is
November 13, 2015
November 13, 2015
Determine if each function is a direct variation, stating the constant
of variation for those which qualify.
y = 5x
5y = x
y=x+2
3y = 7x
y+8=x
y = x - 11
3y + 1 = 2x
y = -6x
November 13, 2015
Writing an Equation Given a Point
Write an equation of the direct
variation that includes the point (4, -3).
y = kx
Start with the function form of the direct
variation.
-3 = k(4) Substitute 4 for x and -3 for y.
y = kx
Divide by 4 to solve for k.
Substitute the value of k into the original formula.
November 13, 2015
Write the equation of the direct variation that includes each of the
following points;
(1, 2)
(8, 8)
(4, 3)
(3, - 7)
November 13, 2015
Real-World Problem Solving
Your distance from lightning varies directly
with the time it takes you to hear thunder.
If
you hear thunder 10 seconds after you see
the lightning, you are about 2 miles from
the lightning. Write an equation for the
relationship between time and distance.
November 13, 2015
One of the tables below represents a direct variation.
Which one do you think it is and why?
State whether either of the tables below represent a
direct variation. If the table does represent a direct
variation, name the constant of variation.
November 13, 2015
Is each equation a direct variation?
If it is, find the constant of
variation.
1. y = 5x
2. 8x + 2y = 0
3. y = 2x + 5
4. 8x + 4y = 12
5. 6x - 3y = 0
6. x - 3y = 6
November 13, 2015
The ordered pairs in each exercise
are for the same direct variation.
Find each missing value.
7. (3, 2) and (6, y)