DIRECT OR PARTIAL VARIATION
Which equation represents a direct variation?
A. y=3x+5y=3x+5
B. y=3xy=3x
C. y=3x−2y=3x-2
D. y=3x+1y=3x+1
Answer: What is y=3xy=3x?
Find the slope of the line passing through (2,3) and (4,7)
m=2
Find the first differences:
x y
1 5
2, 9
3, 13
4, 17
5, 21
4
The yy-value increases by 15 when the xx-value increases by 5. What is the rate of change?
3
What is the equation of a line with slope 3 and y-intercept 5?
y=3x+5
Identify the type of variation:
y=7x+4
partial variation
Find the slope of the line passing through (−2,5) and (3,15).
m=2
A gym charges a $20 registration fee and $10 per month. Write an equation for the total cost after mm months.
C=10m+20
A car travels 240 km in 4 hours at a constant rate. What is its rate of change?
60 km/h
What is the equation of a line with slope −2 and y-intercept 8?
y=−2x+8
A taxi charges a $5 starting fee plus $2 per kilometre. Is this direct or partial variation?
partial variation
What is the slope of the line represented by
y=−4x+7?
-4
A water tank contains 120 L initially. Water is added at 8 L/min.
a) Write an equation for the volume after tt minutes.
b) How much water is in the tank after 25 minutes?
c) Is this direct or partial variation?
V=8t+120
320 L
and partial variation
A candle decreases from 25 cm to 17 cm in 4 hours. What is its rate of change?
-2 cm/hour
A line has slope 4 and passes through (2,11). What is its equation?
y=4x+3
For the direct variation
y=4.5x
what is the constant of variation?
4.5
A line passes through (1,8) and (5,20). What is its slope?
m=3
The x-values increase by 2 each time, while the y-values are:
7, 13, 19, 25
What is the rate of change?
3
The cost of 5 notebooks is $20. The cost of 9 notebooks is $36. What is the rate of change of cost per notebook?
$4 per notebook
Use the table to determine the equation.
x y
1 7
2 10
3 13
y=3x+4
The table shows a direct variation.
x y
2 10
4 20
6 30
8 40
Find the constant of variation and write the equation.
k=5
y=5x
A line has a slope of −3 and passes through (2,7)(2,7). What is the equation of the line?
y=−3x+13?
For this table, determine the first difference and the rate of change.
x y
0 12
2 20
4 28
6 36
first difference = 8 and rate of change = 4
A water tank contains 800 L of water. After 5 hours, it contains 650 L. Assuming a constant rate, what is the rate of change?
-30 L/hour
A relation has a rate of change of 2.5 and passes through (4,15). What is its equation?
y=2.5x+5