Homework (Tuesday, 11/17)
Lesson 3.08 packet
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/direct-variation/directvariation-definition/constant-of-variation-definition
Per 3: Extra Credit for no
missing assignments
Trevor, Jonathan, Angie, Briana, Paul, Teo,
Arenui, Maya, Karen, Arman, Pejhon,
Naylie, Victoria, Jamie
Per 4: Extra Credit for no
missing assignments
Hamzeh, Francisco, Nathan, Arthur, Jose,
Monaghan, Charli, Ashley, Alejandro,
Daisy, Ava, Preston, Alexis, Ana, Katelyn,
Sebastian, Oliver, Andrea
Per 5: Extra Credit for no
missing assignments
Azam, Sean B, Luis, Carly, Caroline G,
Peyton, Karina, Kimberly, Nikki, Jennifer
P, Abby, Sofia, Nan, Annabelle, Morgan,
Jacob
Lesson 3. 08
Direct and
Inverse
Variations
Direct Variation
•a relationship where as x increases and y
increases or x decreases and y decrease at
a CONSTANT RATE.
•Formula: y = kx, where k cannot be zero and
k is called constant variation
What does the graph y=kx look like?
A straight line with a y-intercept of 0.
f x  = 3 x
y=3x
5
-10
10
-5
Looking at the graph, what is the slope of the line?
Answer: 3
Looking at the equation, what is the
constant of variation?
Answer: 3
The constant of variation and the slope are
the same!!!!
Direct Variation
Direct variation uses the following formula:
y1 y 2

x1 x 2
Direct Variation
Example 1: if y varies directly as x
and y = 10 as x = 2.4, find x when y =15.
Direct Variation
•If y varies directly as x and y = 10
find x when y =15.
•y = 10, x = 2.4
make these y1 and x1
•y = 15, and x = ?
make these y2 and x2
Direct Variation
• if y varies directly as x and y =
10 as x = 2.4, find x when y =15
10 15

2.4
x
Direct Variation
•How do we solve this?
Cross multiply and set
equal.
10 15

2.4
x
Direct Variation
•We get: 10x = 36
•Solve for x by diving both sides by
10.
•We get x = 3.6
Direct Variation
Example 2: If y varies directly with x and
y = 12 when x = 2, find y when x = 8.
Direct Variation
•If y varies directly with x and
y = 12 when x = 2, find y when
x = 8.
12 y

2 8
Direct Variation
12 y

2 8
•Cross multiply: 96 = 2y
•Solve for y.
48 = y.
Inverse Variation
Inverse is very similar to direct, but in
an inverse relationship as one value goes
up, the other goes down. There is not
necessarily a constant rate.
𝒌
,
𝒙
Formula: 𝐲 = where k cannot be zero
and k is called constant inverse variation
Inverse Variation
In Inverse variation we will
Multiply them.
x1y1 = x2y2
What does the graph of xy=k
look like? Let k=5 and graph.
𝟓
𝐲=
𝒙
f x  =
5
6
x
4
2
-10
-5
5
-2
-4
-6
10
This is a graph of a hyperbola.
Notice: That in the graph, as the x
values increase the y values decrease.
Also, as the x values decrease the y
values increase.
Inverse Variation
Example 3: If y varies inversely with x and
y = 12 when x = 2, find y when x = 8.
x1y1 = x2y2
2(12) = 8y
24 = 8y
y=3
Inverse Variation
Example 4: If y varies inversely as x and x = 18
when y = 6, find y when x = 8.
18(6) = 8y
108 = 8y
y = 13.5