Question

answer the following questions pertaining to the table

• is this relationship proportional?
• if so, what is the constant of proportionality?
• write the equation for this relationship.
• if you were going to plot the unit rate as a coordinate point, then it would be ...( , ).
• if you graphed this relationship, would it go through the origin?

the table is:

pounds of apples	5	12	15	20
cost ($)	15	36	45	60

Explanation:

Step1: Check proportionality

Calculate $\frac{\text{Cost}}{\text{Pounds}}$ for each pair:
$\frac{15}{5}=3$, $\frac{36}{12}=3$, $\frac{45}{15}=3$, $\frac{60}{20}=3$
All ratios are equal, so the relationship is proportional.

Step2: Identify constant of proportionality

The constant is the equal ratio calculated: $k=3$

Step3: Write the equation

Let $C$ = cost, $p$ = pounds. Proportional equation: $C = kp$
Substitute $k=3$: $C=3p$

Step4: Find unit rate coordinate

Unit rate is cost per 1 pound. When $p=1$, $C=3(1)=3$, so the point is $(1, 3)$

Step5: Check if line goes through origin

Proportional relationships have equations of the form $y=kx$, which passes through $(0,0)$ (when $p=0$, $C=0$). So it goes through the origin.

Answer:

1. Yes, this relationship is proportional.
2. The constant of proportionality is 3.
3. The equation is $C=3p$ (where $C$ is cost in dollars, $p$ is pounds of apples).
4. The unit rate coordinate point is $(1, 3)$.
5. Yes, the graphed relationship would go through the origin.