Homework (Tuesday, 11/17) - PowerPoint Presentation

Slide1

Homework (Tuesday, 11/17)

Lesson 3.08 packet

http://www.virtualnerd.com/algebra-1/linear-equation-analysis/direct-variation/direct-variation-definition/constant-of-variation-definition

Slide2

Per 3: Extra Credit for no missing assignments

Trevor, Jonathan, Angie, Briana, Paul, Teo, Arenui

, Maya, Karen, Arman,

Pejhon

,

Naylie

,

Victoria,

JamieSlide3

Per 4:

Extra Credit for no missing assignmentsHamzeh, Francisco, Nathan, Arthur, Jose, Monaghan, Charli, Ashley, Alejandro, Daisy, Ava, Preston, Alexis, Ana, Katelyn, Sebastian

, Oliver, Andrea Slide4

Per 5:

Extra Credit for no missing assignmentsAzam, Sean B, Luis, Carly, Caroline G, Peyton, Karina, Kimberly, Nikki, Jennifer P, Abby, Sofia, Nan, Annabelle, Morgan,

JacobSlide5

Lesson 3. 08

Direct

and Inverse

VariationsSlide6

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 Slide7

What does the graph y=

kx

look like?

A straight line with a y-intercept of 0

.

y

=3xSlide8

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!!!!Slide9

Direct Variation

Direct variation uses the following formula:Slide10

Direct Variation

Example 1:

if

y varies

directly

as x

and y = 10 as x =

2.4, find

x when y =15.Slide11

Direct Variation

If y varies directly as x and y = 10

find x when y =15.

y = 10, x = 2.4

make these y

1

and x

1

y = 15, and x = ?

make these y

2

and x

2Slide12

Direct Variation

if y varies directly as x and y = 10 as x = 2.4, find x when y =15Slide13

Direct Variation

How do we solve this? Cross multiply and set equal.Slide14

Direct Variation

We get: 10x = 36

Solve for x by diving both sides by 10.

We get x = 3.6Slide15

Direct Variation

Example 2:

If

y varies

directly

with x

and

y

=

12 when

x = 2,

find

y when x = 8.Slide16

Direct Variation

If y varies directly with x and y = 12 when x = 2, find y when x = 8.Slide17

Direct Variation

Cross multiply: 96 = 2y

Solve for y. 48 = y.Slide18

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.

Formula:

, where k cannot be zero and k is called constant

inverse variation

 Slide19

Inverse Variation

In

Inverse variation

we will

Multiply

them.

x

1

y

1

= x

2

y

2Slide20

What does the graph of

xy

=k look like? Let k=5 and graph.

 Slide21

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.Slide22

Inverse Variation

Example 3:

If

y

varies inversely

with x and

y

= 12 when x = 2, find y when x = 8.

x

1

y

1

= x

2y

2

2(12) = 8y

24 = 8y

y = 3Slide23

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 = 13.5Slide24
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