CC Math I Standards: Unit 5
DIRECT VARIATION
X
(min)
Y
(gallons)
0
1
2
Introduction: How is slope related to your
shower? A standard shower uses 6 gallons of
water per minute.
 Complete the table based on the
description.
 GRAPH the ordered pairs
3
 What is the SLOPE of the line?
4
The equation turns out to be ___________________________
The number of gallons of water, y, depends directly on the amount of time in the shower, x.
DIRECT VARIATION is described by an equation of the form y
= kx, where k ≠0.
k is called the _______________________________.
Key Phrases:
Looking at our previous example, what do you notice about the slope (m) and constant of variation (k)?
Notice: the ordered pair (0, 0) is a solution of y = kx.
GRAPH each direct variation equation.
Equation
y = 4x
y = - 1/3 x
SLOPE as a
ratio
START at the Origin (0,0)
From Point (0, 0), move the RISE and RUN.
Rise: Positive =___________, Negative = ___________
Run: Positive =___________, Negative = ____________
Draw a dot.
Draw a line Connecting the Two Dots.
Graph the following direct variation equations
#1: y = 5/4 x
RISE = _______ RUN = ________
Directions:
#2: y = - 3/5 x
RISE = _______ RUN = ________
Directions:
#3: y = 1/2x
RISE = _______ RUN = ________
Directions:
Find the equation of a Direct Variation situation:
Step 1: SUBSTITUTE the x-value and y-value of a point in direct variation equation
Step 2: SOLVE for k.
Step 3: REWRITE the equation with the value of k and variables x and y.
1) Suppose y varies directly as x, and y = 28 when x = 7. Write a direct
variation equation.
2) Suppose y varies directly with x, and y = 9 and x = -3. Write a direct
variation equation.
3) Suppose that y varies directly as x, and x = 4 and y = 10. Write a direct
variation equation.
4) Suppose that y varies directly as x, and x = 16 when y = 4. Write a direct
variation equation.
5) Suppose that y varies directly with x, and y = - 12 when x = 15. Write a
direct variation equation.
6) A flock of geese migrated 375 miles in 7.5 hours and suppose that the miles
traveled varies directly with the time. Write a direct variation equation
relating time travelled with distance traveled.
7) The weight of an object on the moon varies directly with its weight on earth.
A 360-poung object on Earth, but weighed only 60 pounds on the moon. Write
an equation that relates the weight on the moon m with the weight on Earth e.