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---