Direct and Inverse Variation, Slope

direct variation

Linear function that uses the equation, y=kx, and always passes through the origin (0,0); typically, as x increases, y increases (proportional relationship)

The slope of the line is 9/5

( 1 , 2 ) and ( 6 , 11) are two points on a line. What is the slope of the line? Hint: point 1 (x,y) point 2 (x,y)

The slope is 3/4

( 3 , 2 ) and ( 7 , 5 ) are two points on a line. What is the slope of the line? Hint: point 1 (x,y) point 2 (x,y)

The slope is -1/2

Find the slope of this graph.

The slope is -4/1

Find the slope of this graph.

The slope is 1/3

Find the slope of this graph.

The slope is 3/2

Find the slope of this graph.

20

If a car uses 8L of gas to travel 160km, how much gas will the car use to travel 400km?

1/2

If y varies directly as x, and y=2 when x=8, what is y when x=2?

10

If y varies directly as x, and y=50 when x=4, what is x when y=125?

6

If y varies inversely as x, and y=20 when x=3, what is x when y=10?

15

If y varies inversely as x, and y=9 when x=5, what is y when x=3?

5

It takes a factory 10 days to produce 10,000 cars. How many days would it take two factories to produce the same number of cars?

105

Johnny makes $15 for every two days he delivers newspapers. How much would he make after two weeks?

inverse variation

Non-linear function that uses the equation, y=k/x, and never passes through (0,0) or crosses the axes; typically, as x increases, y decreases (decreasing decrease)

zero

The slope of a horizontal line is _______________.

positive

The slope of the line is: A. positive B. negative C. undefined D. zero

negative

The slope of the line is: A. positive B. negative C. undefined D. zero

undefined

The slope of this line is: A. positive B. negative C. zero D. undefined

The slope is 1/7

The slope of this table is

The slope is 12

The slope of this table is

The slope is 2

The slope of this table is

vertical line

This is a _________________ line. A. horizontal B. vertical

horizontal line

This is a __________________ line. A. horizontal B. Vertical

180

Three pipes take 1 hour to water the football field. How many minutes would it take one pipe to water the field?

The slope is 4.

What is the slope of this line? Hint: RISE over RUN

The slope is undefined.

What is the slope of this line? Hint: RISE over RUN Hint: Vertical line

The slope is ZERO.

What is the slope of this line? Hint: RISE over RUN Hint: horizontal line

-2

What is the slope of this line? Hint: RISE over RUN

divide y/x

how to find the constant of variation (k) for a direct variation

multiply xy

how to find the constant of variation (k) for an inverse variation

constant of variation

k; shows the relationship between the x-value and y-value in direct and inverse variations

direct variation equations

y=3x; 4x+y=0; y=1/2x; y=0.4x; y=x/8; 2x=6y are examples of---

inverse variation equations

y=7/x; xy=9; y=-5/x are examples of---