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Read the description of a proportional relationship. $\newline$ Luther is starting a summer camp for children who are deaf or hard of hearing. He needs to hire enough counselors to chaperone the children. There is a proportional relationship between the number of counselors Luther hires, $x$ , and the maximum number of children who can attend the camp, $y$ . $\newline$ By law, if Luther hires $2$ counselors, then at most $10$ children can attend the camp. Write the equation for the relationship between $x$ and $y$ . $\newline$ $y = \_$

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Write and solve equations for proportional relationships

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Q. Read the description of a proportional relationship.

\newline

Luther is starting a summer camp for children who are deaf or hard of hearing. He needs to hire enough counselors to chaperone the children. There is a proportional relationship between the number of counselors Luther hires,

x

, and the maximum number of children who can attend the camp,

y

.

\newline

By law, if Luther hires

2

counselors, then at most

10

children can attend the camp. Write the equation for the relationship between

x

and

y

.

\newline

y = \_

Understand Proportional Relationship: First, we need to understand the proportional relationship given. We know that for every $2$ counselors, $10$ children can attend. This sets up a ratio of counselors to children as $2:10$ , which simplifies to $1:5$ .
Find Equation for Relationship: To find the equation that describes this relationship, we use the simplified ratio. If $1$ counselor allows $5$ children, then $x$ counselors would allow $5$ times $x$ children. So, the equation is $y = 5x$ .

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