Modeling Proportional Relationships - Pre Algebra

1. Five pounds of apples cost 15 dollars, and cost is proportional to weight. What equation gives cost $y$ for $x$ pounds?

   $y = 3x$. The unit rate is 15 dollars divided by 5 pounds, or 3 dollars per pound.

2. In a proportional relationship, $y = 9$ when $x = 3$. What is $y$ when $x = 7$?

   $21$. The constant is $\frac{9}{3} = 3$, so $y = 3 \cdot 7$.

3. What equation form models a proportional relationship?

   $y = kx$, where $k$ is the constant of proportionality (the unit rate).

4. How do you find the constant of proportionality from a pair $(x, y)$ with $x \ne 0$?

   Divide: $k = \frac{y}{x}$.

5. In $d = 60t$, $d$ is miles traveled after $t$ hours. What does $60$ represent?

   The constant speed: $60$ miles per hour.

6. In $y = 4x$, $y$ is the cost in dollars of $x$ notebooks. What does the point $(1, 4)$ mean?

   One notebook costs 4 dollars. The point where $x = 1$ shows the unit rate.

7. Using $y = 2.5x$, what is $y$ when $x = 8$?

   $20$. Compute $2.5 \times 8$.

8. A worker earns 12 dollars per hour. What equation gives pay $p$ after $h$ hours?

   $p = 12h$. Pay is proportional to hours, with unit rate 12 dollars per hour.

9. What does the graph of a proportional relationship look like?

   A straight line through the origin $(0, 0)$.

10. The point $(5, 30)$ lies on the graph of a proportional relationship. What is the constant of proportionality?

    $6$. Compute $\frac{30}{5}$.

11. A proportional table has $x$-values $2$, $4$, $6$ and $y$-values $7$, $14$, $21$. What equation models it?

    $y = 3.5x$. Each ratio $\frac{y}{x}$ equals $3.5$.

12. A proportional table has $x$-values $3$, $6$, $9$ and $y$-values $1$, $2$, $3$. What equation models it?

    $y = \frac{1}{3}x$. Each ratio $\frac{y}{x}$ equals $\frac{1}{3}$.

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