### Direct Variation

```
Equation of Direct Variation

When you see: “y varies direcly as x”
write
 Write
the equation of direct variation
that has a coefficient of variation
equal to -3
 Replace
k with -3
 Assume
y varies directly as x. If the
coefficient of variation is ½, then what
is the value of y when x = -6?
 Replace
k with ½
 Replace x with -6
 Multiply ½ times -6 to get answer

Assume y varies directly as x. If the
coefficient of variation is 4, then what is
the value of x when y = 6?
Replace k with 4 and y with 6
 Divide 4 on both sides
 Reduce the fraction

Suppose y varies directly as x. If y = 3
when x = 15, then find x when y = 5.
2. Suppose y varies directly as x. Find x
when y = 10 if y = -7 when x = -14.
3. Suppose y varies directly as x. If x = 15
when y = 12, find x when y = 21.
4. Suppose y varies directly as x. If x = 24
when y = 8, then what is the coefficient
of variation?
1.

The amount of a person’s paycheck
varies directly with the number of hours
worked. For 13 hours of work, the
paycheck is \$73.45. Find the pay for 25
hours of work.
“varies directly” means:
 Remember, “y” always varies directly as
“x”


The amount of a person’s paycheck
varies directly with the number of hours
worked. For 13 hours of work, the
paycheck is \$73.45. Find the pay for 25
hours of work.

If “y” varies directly as “x” than what
comes before varies directly is y and
what comes after it is x

The amount of a person’s paycheck
varies directly with the number of hours
worked. For 13 hours of work, the
paycheck is \$73.45. Find the pay for 25
hours of work.

Replace paycheck with \$73.45 and
hours with 13
Divide both sides by 13
 Plug k back into the equation


The amount of a person’s paycheck
varies directly with the number of hours
worked. For 13 hours of work, the
paycheck is \$73.45. Find the pay for 25
hours of work.
The question asks for how much you’d
make in 25 hours, so replace x with 25


The amount of a person’s paycheck
varies directly with the number of hours
worked. For 13 hours of work, the
paycheck is \$73.45. Find the pay for 25
hours of work.
K = 5.65 which is how much this person
makes per hour.
 For 25 hours, this person makes \$141.25


The number of calories in a container of
milk is directly proportional to the
amount of milk in the container. If there
are 160 calories in an 8-ounce glass of
milk, find the number of calories in a 15ounce glass of milk.

Directly proportional means direct
variation

The number of calories in a container of
milk is directly proportional to the
amount of milk in the container. If there
are 160 calories in an 8-ounce glass of
milk, find the number of calories in a 15ounce glass of milk.

Y varies directly as x, so calories is y and
amount of milk is x

The number of calories in a container of
milk is directly proportional to the
amount of milk in the container. If there
are 160 calories in an 8-ounce glass of
milk, find the number of calories in a 15ounce glass of milk.

Calories is 160 and the amount of milk is
8
Divide both sides by 8
 Plug k back into the equation


The number of calories in a container of
milk is directly proportional to the
amount of milk in the container. If there
are 160 calories in an 8-ounce glass of
milk, find the number of calories in a 15ounce glass of milk.
K means 20 calories per ounce
 Plug in 15 for x to solve the problem
 Multiply to solve


The number of calories in a container of
milk is directly proportional to the
amount of milk in the container. If there
are 160 calories in an 8-ounce glass of
milk, find the number of calories in a 15ounce glass of milk.

There are 300 calories in a 15-ounce
glass of milk

Laura typed 176 words correctly in 4
minutes. Assuming a direct variation,
how many words can she type in 30
minutes?

A refund you get varies directly as the
number of cans you recycle. If you get a
\$3.75 refund for 75 cans, how much
should you get for 500 cans?
The number of miles driven varies directly
with the number of gallons of gas used. Erin
drove 297 miles on 9 gallons of gas. How far
would she be able to drive on 14 gallons of
gas?
 The kinetic energy of a car varies directly
with the square of the velocity of the car. A
car with a velocity of 9 meters per second
has 33,100 joules of kinetic energy. About
how much kinetic energy does the same
car have when traveling at 12 meters per
second?


The height of a kite from the ground
varies directly with the cube of the wind
speed. A kite flies 8 feet high when the
wind speed is 10 miles per hour. What is
the height of a kite when the wind speed
is 25 miles per hour?
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