3­2 Direct variation.notebook
November 08, 2016
3­2 Direct Variation
Direct Variation is a special type of linear relationship in which the y­
intercept is 0 or the origin
If the ratio of two variables is constant, then the variables have a special relationship, known as direct variation.
A direct variation relationship can be represented by a function in the form , where .
­ The line passes through (0, 0) and the slope of the line is The coefficient of variation for a direct variation is the coefficient of x which is . By dividing each side of , you can see that the ratio of the variables is constant for all x/y pairs:
Identify the coefficient of variation and graph the line.
3­2 Direct variation.notebook
November 08, 2016
Write a direct variation equation that relates the two variables and solve.
1. Suppose y varies directly as x, and y=15 when x=­6. Find y when x=8.
2. Suppose y varies directly as x, and y=7 when x=14. Find y when x=­3.
3. Suppose y varies directly as x, and y=1 when x=­0.25. Find y when x=­5.
Weight on Mars, y, varies directly with weight on Earth,x. The weight of an atmospheric sensor is 130 lbs on earth and on Mars it is 50 lbs.
Write a direct variation equation that relates the weights on Earth and on Mars.
What is the weight of a 100 lb person?
What is the weight of a 150 lb person?
3­2 Direct variation.notebook
November 08, 2016
The amount of blood (y) in a person's body varies directly with body weight (x). A person who weighs 160 lbs has about 4.6 qts of blood. About how many quarts of blood are in the body of a 185 lb person?
What is the constant of variation?
What is the equation that relates quarts of blood to weight?
Determine the solution.
Write a direct variation equation that relates the two variables and solve.
1. The number of calories the cereal contains varies directly with the number of ounces of cereal. A cereal has 120 calories for a 4­ounce serving. Write a direct variation equation for the relationship between amount of cereal and number of calories. How many calories would be in an 18­ounce box?
2. The number of tablespoons of sea salt needed in a saltwater aquarium varies directly with the number of gallons of water in the tank. A pet shop owner recommends 100 tablespoons of sea salt to a 20 gallon tank. Write a direct variation equation for the relationship between the size of the tank and the amount of salt. How many tablespoons of sea salt should be added to a 25 gallon tank?