final Revision sheet g8

In a direct variation, y=39 when x=3.  Find the value of y when x=2.

• 26

• 3

• 58.5

• 2

Answer explanation

In direct variation, y = kx. Given y = 39 when x = 3, k = 39/3 = 13. For x = 2, y = 13 * 2 = 26. Thus, the value of y when x = 2 is 26.

 y varies directly with x, and y is 16 when x is 32. Which equation represents this situation?

• y=32x

• y=16x

• y=2x

• y=(1/2)x

Answer explanation

Since y varies directly with x, we can express this as y = kx, where k is the constant of variation. Given y = 16 when x = 32, we find k = 16/32 = 1/2. Thus, the equation is y = (1/2)x.

Is this a direct variation?

• yes

• no

Answer explanation

Yes, this is a direct variation because it follows the form y = kx, where k is a constant. In direct variation, as one variable changes, the other changes proportionally.

If y = 15 when x = 12 find y when x = 32.

• y = (5/4)x; 40

• y= (4/5)x; -40

• y= 4x; 5

• y= 5x; -5

Answer explanation

Given y = 15 when x = 12, the ratio y/x = 15/12 = 5/4. Thus, y = (5/4)x. For x = 32, y = (5/4) * 32 = 40. Therefore, the correct choice is y = (5/4)x; 40.

What does the Direct Variation Equation look like?

• Y= kx

• y = mx + b

• y = b

• y = x

Answer explanation

The Direct Variation Equation is represented as Y = kx, where k is a constant. This shows that Y varies directly with x. The other options represent different types of equations, not direct variation.

If y vaires directly with x and y= 12 when x= 15. What is the value of x when y= 16?

• 12.8

• 20

• 11.25

• 19

Answer explanation

Since y varies directly with x, we can use the formula y = kx. Given y = 12 when x = 15, we find k = 12/15 = 0.8. To find x when y = 16, we set 16 = 0.8x, leading to x = 20. Thus, the correct answer is 20.

In a direct variation, y=39 when x=3.  Find the value of y when x=2.

• 26

• 3

• 58.5

• 2

Answer explanation

In direct variation, y = kx. Given y = 39 when x = 3, k = 39/3 = 13. For x = 2, y = 13 * 2 = 26. Thus, the value of y when x = 2 is 26.

Write the equation for the table given.

• y = 1/3x

• y = 3x

• y = 1/2x

Answer explanation

To find the equation, we look for a linear relationship in the table. The correct choice, y = 3x, indicates that for every increase of 1 in x, y increases by 3, matching the values in the table.

What is the constant of proportionality (in miles per hour) based on the table?

• 45

• 90

• 135

• 2

Answer explanation

The constant of proportionality is found by dividing the distance by the time. If the table shows a distance of 90 miles and a time of 2 hours, then 90/2 = 45 miles per hour, making 45 the correct answer.

The value of y varies directly with x.  Which function represents the relationship between x and y if y = 14 when x = 6. 

• y=20x

• y=84x

• y=7/3x

• y=3/7x

Answer explanation

Since y varies directly with x, we can express this as y = kx, where k is a constant. Given y = 14 when x = 6, we find k = 14/6 = 7/3. Thus, the function is y = 7/3x.