1. $y$ is directly proportional to $x$. When $x=4$, $y=18$. Find the constant $k$.

Answer: $k=4.5$.

2. $y$ is directly proportional to $x$, and $y=21$ when $x=7$. Find $y$ when $x=12$.

Answer: $y=36$.

3. $y$ is proportional to $x^2$. When $x=3$, $y=45$. Find $y$ when $x=5$.

Answer: $125$.

4. $V$ is proportional to $r^3$. $V=54$ when $r=3$. Find $V$ when $r=2$.

Answer: $V=16$.

5. A machine fills 84 bottles in 6 minutes. How many does it fill in 15 minutes at the same rate?

Answer: 210 bottles.

6. A directly proportional graph contains $(5,35)$. Find $y$ when $x=9$.

Answer: $63$.

7. $p$ varies directly as $q$. If $p=16$ when $q=2$, write $p$ in terms of $q$.

Answer: $p=8q$.

8. $y$ is proportional to $x$. Given $y=32$ when $x=8$, find $x$ when $y=54$.

Answer: $x=13.5$.

9. $A$ is proportional to $r^2$. $A=28$ when $r=2$. Find $A$ when $r=5$.

Answer: $175$.

10. A car travels 156 km in 2 hours at constant speed. How far in 3.5 hours?

Answer: 273 km.

11. A learner says a direct proportion can have a non-zero value when $x=0$. Is this correct?

Answer: No. Direct proportion has the form $y=kx$, so $y=0$ when $x=0$.

12. $z$ is proportional to $t^3$. $z=16$ when $t=2$. Find $z$ when $t=4$.

Answer: $128$.

13. A table shows a direct relationship with ratio $y:x=2:5$. Work out $y$ when $x=15$. Choose an equivalent-ratio or constant-multiplier method and give a reason.

Answer: $y=6$. Both parts of the ratio scale by 3, so $y:x=6:15$.