Question

Erik wants to make lemonade for his friends. He used $4$ tablespoons of lemon juice for $6$ glasses of lemonade. Then he uses 8 tablespoons of lemon juice for $12$ glasses.
Which of the following is correct for the context given?

P. The number of tablespoons used and the number of glasses are in a proportional relationship.
Q. The number of tablespoons used and the number of glasses are not in a proportional relationship.

• A. $P$ and $R$
• B. $Q$ and $R$
• C. $P$ and $Q$
• D. $P,Q,$ and $R$

Answer 1

The correct option is A $P$ and $R$

$4$ tablespoons of lemon juice: $6$ glasses of lemonade
$8$ tablespoons of lemon juice:$12$ glasses of lemonade

We know that,
$\to$ A proportion is a statement that two ratios are equivalent to each other.
Let us check.

$\frac{6}{4}=\frac{3}{2}$

$\frac{12}{8}=\frac{3}{2}$


The ratios are equal, so the ratios form a proportion.
Therefore, they are given in proportional relation. Option P is correct and Option $Q$ is incorrect.

Let us check Option $R$.
We know that,

$\to$ The graph of a proportional relationship between x and y is a straight line passing through the origin $(0,0)$.

We could see that the graph is a straight line passing through the origin and the points marked in the graph $(4,6)$ and $(8,12)$ are correct.

Therefore, Option $R$ is also correct.

$\to$ Option D is correct.