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Read the description of a proportional relationship. $\newline$ Scott loves to play the piano but doesn't like practicing the exercises his piano teacher assigns. Scott knows the exercises will help him play better though, so he tries to motivate himself using his favorite treat \mdash chocolate chip cookies. There is a proportional relationship between the amount of time (in hours) that Scott practices the piano, $x$ , and how many cookies he gives himself, $y$ . $\newline$ When Scott practices for $1$ hour, he gives himself $4$ cookies. 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

Scott loves to play the piano but doesn't like practicing the exercises his piano teacher assigns. Scott knows the exercises will help him play better though, so he tries to motivate himself using his favorite treat \mdash chocolate chip cookies. There is a proportional relationship between the amount of time (in hours) that Scott practices the piano,

x

, and how many cookies he gives himself,

y

.

\newline

When Scott practices for

1

hour, he gives himself

4

cookies. Write the equation for the relationship between

x

and

y

.

\newline

y = \_

Identify Given Values: Step $1$ : Identify the given values from the problem: $\newline$ Time practiced, $x = 1$ hour $\newline$ Number of cookies, $y = 4$ $\newline$ Calculate the constant of proportionality, $k$ . $\newline$ $k = \frac{y}{x}$ $\newline$ $k = \frac{4}{1}$ $\newline$ $k = 4$
Calculate Constant: Step $2$ : Use the constant of proportionality to write the equation for the proportional relationship. $\newline$ Since $k = 4$ , the equation is: $\newline$ $y = kx$ $\newline$ $y = 4x$

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