Direct Variation Guided Notes
A linear relationship is called a _________ _____________
It looks like:
when the ratio of y coordinate to x coordinate is __________.
We say y varies directly with x.
Important: Direct Variation Equations Always Go Through The ____________.
Therefore, their y-intercept will always be ____.
First, check to see if you have a direct variation, or just a linear equation.
- On a graph, just look to see if it does through the ___________.
- With points or a table (which are points by the way), find the ratio of _______________.
If the ratio is constant, it’s a direct variation. **Hint, the constant ratio is also the _________.
I have a direct variation, now what?
If you have a graph,:
What’s the deal with m?
If you have y and x:
1. Plug y and x into y=mx.
1. Find the slope
2. Solve for m.
2. Plug the slope in for m.
3. Plug m into y = mx.
If you have points/table:
1. The ratio is slope
2. Plug m into y = mx.
slope, constant rate of
change, constant of
proportionality, unit
rate…… All these names
mean the
_______________!
Graph:
Points:
(-3,9), (-2,6)
Table:
equation: ______________
equation: ______________
x
y
0
0
6
3
10
5
16
8
equation: ___________
If y varies directly with x, write a direct variation equation for when y = 10 and x = 3.
If a varies directly with b, write a direct variation equation for when a = 1 and b = 7.
If m varies directly with n, write a direct variation equation for when m = 6 and n = 2. Find n when m = 12.
FIN
AL
AN
SW
ER
Words:
1.
x = weight on Earth = _______
2.
3.
______ = m _______
y = _____ x
y = weight on Titan = _______
A car drives 280 miles in 5.5 hours. Assuming
that the distance traveled varies directly with
the time traveled, write a direct variation
equation. How far will the car travel in 7 hours?
Tell whether the table is a direct variation or not.
If so, write a direct variation equation to match the
table.
x
y
x
y
15
3
-2
-8
5
1
4
16
25
5
0
0
50
10
-8
32
Direct Variation Guided Notes
A linear relationship is called a _________
direct _____________
variation
It looks like:
when the ratio of y coordinate to x coordinate is __________.
constant
y=mx
We say y varies directly with x.
origin
Important: Direct Variation Equations Always Go Through The ____________.
0
Therefore, their y-intercept will always be ____.
First, check to see if you have a direct variation, or just a linear equation.
origin
- On a graph, just look to see if it does through the ___________.
y co-ordinate
x co-ordinate
- With points or a table (which are points by the way), find the ratio of _______________.
slope
If the ratio is constant, it’s a direct variation. **Hint, the constant ratio is also the _________.
What’s the deal with m?
I have a direct variation, now what?
If you have a graph,:
1. Find the slope
2. Plug the slope in for m.
If you have y and x:
1. Plug y and x into y=mx.
2. Solve for m.
3. Plug m into y = mx.
Graph:
slope, constant rate of
If you have points/table:
1. The ratio is slope
2. Plug m into y = mx.
proportionality, unit
rate…… All these names
mean the
same thing
_______________!
Points:
(-3,9), (-2,6)
y = 15/2 x
equation: _____________
change, constant of
y = -3x
equation: _____________
Table:
x
y
0
0
6
3
10
5
16
8
y = 1/2x
equation: ___________
If y varies directly with x, write a direct variation equation for when y = 10 and x = 3.
y = 10/3 x
If a varies directly with b, write a direct variation equation for when a = 1 and b = 7.
a = 1/7 b
If m varies directly with n, write a direct variation equation for when m = 6 and n = 2. Find n when m = 12.
m=3n
n=4
FIN
AL
AN
SW
ER
Words:
1.
105
x = weight on Earth = _______
2.
15
105
______
= m _______
3.
1/7
y = _____
x
15
y = weight on Titan = _______
A car drives 280 miles in 5.5 hours. Assuming
that the distance traveled varies directly with
the time traveled, write a direct variation
equation. How far will the car travel in 7 hours?
y = 50.9 x
356.3 miles in 7 hours.
Tell whether the table is a direct variation or not.
If so, write a direct variation equation to match the
table.
x
y
x
y
15
3
-2
-8
5
1
4
16
25
5
0
0
50
10
-8
32
y = 1/5 x
Not a direct
variation.