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Contents

Algebra I: Variation

Problems

Direct Variation

Inverse Variation

Problem : Could the relationship between the following quantities be represented by a direct variation equation?
a) The amount of time spent running at a steady pace and the number of miles ran
b) Your age a certain number of years from now
c) Your age and your height
d) The number of lawns you mow and the amount of money you make
e) The amount of gas you buy (in gallons) and the amount of money you pay

a) Yes.
b) No, because this variation does not start at (0, 0) -- you are not 0 years old now.
c) No, because people do not grow at a constant rate.
d) Yes. e) Yes.

Problem : If y varies directly as x , and y = 3 when x = 15 , write an equation describing the variation.

y = x

Problem : If r varies directly as q , and r = 10 when q = 6 , write an equation describing the variation.

r = q

Problem : If y varies directly as x , and the constant of variation is 3 , what is y when x = 7 ?

y = 21

Problem : If y varies directly as x , and the constant of variation is , what is x when y = 5 ?

x =

Problem : If y varies directly as x , and y = 6 when x = 8 , what is y when x = 14 ?

x =

Problem : If y varies directly as x , and y = 5 when x = 4 , what is x when y = 15 ?

x = 12

Problem : y varies directly as x , and the constant of variation is . Graph the line which represents the variation, and write an equation that describes the variation.

y = x

Problem : y varies directly as x , and y = 3 when x = 2 . Graph the line which represents the variation, and write an equation that describes the variation.

y = x

Problem : If the following graph represents a direct variation, what is the constant of variation? Write an equation to describe the variation.

y = x


y = x

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