A rectangle has a constant width of 8 inches. Its length, $L$, is increased. Does the perimeter, $P$, of the rectangle vary directly with the length?

Yes, because the perimeter increases as the length increases.

No, because the relationship is not of the form $P=kL$.

Yes, because the relationship is linear.

No, because the width is not zero.

Direct Variation Practice — Grade 7 math

Lesson 6: Direct Variation — Practice Questions

1. Solve the equation $\frac{a}{a-2} = \frac{25}{30}$ for $a$. $a = $ ___.
2. A rectangle has a constant width of 8 inches. Its length, $L$, is increased. Does the perimeter, $P$, of the rectangle vary directly with the length?
- A. Yes, because the perimeter increases as the length increases.
- B. No, because the relationship is not of the form $P=kL$.
- C. Yes, because the relationship is linear.
- D. No, because the width is not zero.
3. The variable $y$ varies directly with $x$. If $y=48$ when $x=8$, what is the constant of variation, $k$? $k = $ ___
4. Which of the following equations shows that $y$ is directly proportional to $x$?
- A. $y = 5x$
- B. $y = x + 5$
- C. $y = \frac{5}{x}$
- D. $y = x^2$
5. Suppose $p$ varies directly with $q$. If $p=21$ when $q=3$, find the value of $p$ when $q=7$. $p = $ ___
6. The total cost, $C$, in dollars for downloading songs varies directly with the number of songs, $n$. If 8 songs cost 12 dollars, what is the cost of 10 songs in dollars? Cost = ___ dollars
7. If $y$ varies directly with $x$, and $x$ is doubled, what is the effect on $y$?
- A. $y$ is halved
- B. $y$ is doubled
- C. $y$ is squared
- D. $y$ does not change
8. The variable $y$ varies directly with $x$. If $y=54$ when $x=9$, what is the constant of variation, $k$? The value of $k$ is ___.
9. The total cost, $C$, of buying gasoline varies directly with the number of gallons, $g$. If 10 gallons of gas cost 40 dollars, which equation models this relationship?
- A. $C = 4g$
- B. $C = 0.25g$
- C. $g = 4C$
- D. $C = 10g$
10. The distance a spring stretches, $s$, varies directly with the mass, $m$, attached to it. A mass of 4 kg stretches the spring by 12 cm. How far will a mass of 7 kg stretch the spring? The spring will stretch ___ cm.