How do you graph a direct variation
2 answers:
When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation.
In simpler terms, that means if A is always twice as much as B, then they directly vary. If a gallon of milk costs $3, and I buy 1 gallon, the total cost is $3. If I buy 10 gallons, the price is $30. In this example the total cost of milk and the number of gallons purchased are subject to direct variation -- the ratio of the cost to the number of gallons is always 3.
To be more "geometrical" about it, if y varies directly as x, then the graph of all points that describe this relationship is a line going through the origin (0, 0) whose slope is called the constant of variation. That's because each of the variables is a constant multiple of the other, like in the graph shown below:
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Answer:
skis and
snowboards were rented.
Step-by-step explanation:
Let the number of skis rented be and the number of snowboards rented be
.
If a total of people rented on a certain day, then the total number of skis and snowboards rented that particular day is also
.
This gives us the equation
.
If skis cost $ , then
number of skis cost $
.
If snowboards cost $ , then
number of snowboards cost $
.
The total cost will give us another equation,
From equation (1),
.
We put equation (3) into equation (2) to get,
We expand the brackets to obtain,
We group like terms to get,
This implies that,
We divide both sides by to get,
We put into equation (3) to get,
Therefore skis and
snowboards were rented.