y=kx & Constant of Proportionality - Pre Algebra

1. What is the constant of proportionality in $y = 7x$?

   $7$. The equation has the form $y = kx$ with $k = 7$.

2. The pairs $(2, 9)$ and $(4, 18)$ come from a proportional relationship. What is the constant of proportionality?

   $4.5$. $\frac{9}{2} = \frac{18}{4} = 4.5$.

3. The graph of $y = kx$ passes through $(5, 2)$. What is $k$?

   $\frac{2}{5}$. $k = \frac{y}{x} = \frac{2}{5}$.

4. Which has the greater constant of proportionality: $y = 0.75x$ or $y = \frac{4}{5}x$?

   $y = \frac{4}{5}x$. Its constant is $0.8$, which is greater than $0.75$.

5. In the equation $y = kx$, what is $k$ called, and how is it found from a pair of values?

   The constant of proportionality. It equals $\frac{y}{x}$ for any pair with $x \ne 0$.

6. In the equation $C = kp$, where $C$ is cost and $p$ is pounds, what does $k$ represent?

   The price per pound, which is the unit rate of the relationship.

7. Pay is proportional to hours worked, and 5 hours earns 60 dollars. Which equation relates pay $p$ to hours $h$?

   $p = 12h$. The constant is $\frac{60}{5} = 12$ dollars per hour.

8. For $y = 0.4x$, what is $x$ when $y = 10$?

   $25$. Solve $0.4x = 10$: $x = 10 \div 0.4 = 25$.

9. How is $k$ related to the graph of $y = kx$?

   $k$ is the slope of the line: each increase of 1 in $x$ raises $y$ by $k$.

10. $y$ is proportional to $x$, and $y = 12$ when $x = 3$. What is the equation?

    $y = 4x$. $k = \frac{12}{3} = 4$.

11. $y$ is proportional to $x$, and $y = 10$ when $x = 4$. What is $y$ when $x = 6$?

    $15$. $k = \frac{10}{4} = 2.5$, so $y = 2.5 \times 6 = 15$.

12. For $y = \frac{2}{3}x$, what is $y$ when $x = 9$?

    $6$. $\frac{2}{3} \times 9 = 6$.

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