Algebra Understanding Direct Variation Quiz

1. If y = 15 when x = 2, then y = 10 when x = 8. True or False?

True

False

The statement is false because based on the given information, as x increases from 2 to 8, y should also increase. However, the statement claims that y decreases from 15 to 10, which contradicts the relationship established by the initial data. Therefore, the answer is false.

Explanation

The statement is false because based on the given information, as x increases from 2 to 8, y should also increase. However, the statement claims that y decreases from 15 to 10, which contradicts the relationship established by the initial data. Therefore, the answer is false.

2. Y is directly proportional to x. If y = 16 when x = 4, write the formula to represent this relation of y and x.

Y = 4x

Y = (1/4)x

Y = 12x

Y = 20x

The formula y = 4x represents the relation between y and x in this scenario. This means that y is directly proportional to x, and for every increase in x by 1 unit, y will increase by 4 units.

Explanation

The formula y = 4x represents the relation between y and x in this scenario. This means that y is directly proportional to x, and for every increase in x by 1 unit, y will increase by 4 units.

3. Assume y varies directly as x. If y = 20 and x = 4, find y when x = 9.

Y = 9/5

Y = 180

Y = 14

Y = 45

Since y varies directly as x, we can set up a proportion to solve for y. The proportion is y/x = k, where k is the constant of variation. We can find k by substituting the given values of y and x into the equation: 20/4 = k. Solving for k, we get k = 5. Now we can use the value of k to find y when x = 9: y/9 = 5. Solving for y, we get y = 45. Therefore, the answer is y = 45.

Explanation

Since y varies directly as x, we can set up a proportion to solve for y. The proportion is y/x = k, where k is the constant of variation. We can find k by substituting the given values of y and x into the equation: 20/4 = k. Solving for k, we get k = 5. Now we can use the value of k to find y when x = 9: y/9 = 5. Solving for y, we get y = 45. Therefore, the answer is y = 45.

4. Which of the following is NOT true about direct variation?

Direct Variation is y = k/x

Direct variation is y = kx

Direct variation always passes through the origin (0,0)

Direct variation has a constant of proportionality, k.

Direct Variation is y = k/x is not true because in direct variation, y is directly proportional to x, meaning that as x increases, y also increases. In the given equation, y is inversely proportional to x, as it decreases when x increases. Therefore, the equation y = k/x does not represent direct variation.

Explanation

Direct Variation is y = k/x is not true because in direct variation, y is directly proportional to x, meaning that as x increases, y also increases. In the given equation, y is inversely proportional to x, as it decreases when x increases. Therefore, the equation y = k/x does not represent direct variation.

5. The amount of money raised at a charity fundraiser is directly proportional to the number of attendees. The amount of money raised for 5 attendees was $100. How much money will be raised for 60 attendees?

$80

$6,000

$1,200

$12,000

The amount of money raised at a charity fundraiser is directly proportional to the number of attendees. This means that as the number of attendees increases, the amount of money raised will also increase. In this case, we are given that for 5 attendees, $100 was raised. To find out how much money will be raised for 60 attendees, we can set up a proportion. If $100 is raised for 5 attendees, then we can find out how much will be raised for 60 attendees by setting up the proportion: 5/100 = 60/x. Solving for x, we find that x is equal to $1,200. Therefore, $1,200 will be raised for 60 attendees.

Explanation

The amount of money raised at a charity fundraiser is directly proportional to the number of attendees. This means that as the number of attendees increases, the amount of money raised will also increase. In this case, we are given that for 5 attendees, $100 was raised. To find out how much money will be raised for 60 attendees, we can set up a proportion. If $100 is raised for 5 attendees, then we can find out how much will be raised for 60 attendees by setting up the proportion: 5/100 = 60/x. Solving for x, we find that x is equal to $1,200. Therefore, $1,200 will be raised for 60 attendees.

6. Which of the following is the correct equation for the following if y varies directly as x? x =3 and y = 4.

Y = (3/4)x

Y = (4/3)x

Y = 1x

Y = -1x

If y varies directly as x, it means that y and x are directly proportional to each other. In other words, as x increases, y also increases in the same proportion. To find the equation that represents this relationship, we can use the formula y = kx, where k is the constant of variation. Given that x = 3 and y = 4, we can substitute these values into the equation and solve for k. By dividing both sides of the equation by 3, we find that k = 4/3. Therefore, the correct equation is y = (4/3)x.

Explanation

If y varies directly as x, it means that y and x are directly proportional to each other. In other words, as x increases, y also increases in the same proportion. To find the equation that represents this relationship, we can use the formula y = kx, where k is the constant of variation. Given that x = 3 and y = 4, we can substitute these values into the equation and solve for k. By dividing both sides of the equation by 3, we find that k = 4/3. Therefore, the correct equation is y = (4/3)x.

7. Katherine sells 75% of the cupcakes that she sells at her bakery. Which term would correctly describe which part of the direct variation equation 75% would represent?

Y variable

X variable

Constant of variation

Product

In a direct variation equation, the constant of variation represents the relationship between the two variables. In this case, the constant of variation would represent the percentage of cupcakes sold by Katherine at her bakery. Since she sells 75% of the cupcakes, this percentage would be the constant of variation in the equation.

Explanation

In a direct variation equation, the constant of variation represents the relationship between the two variables. In this case, the constant of variation would represent the percentage of cupcakes sold by Katherine at her bakery. Since she sells 75% of the cupcakes, this percentage would be the constant of variation in the equation.