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Read the description of a proportional relationship. $\newline$ Sean wants to save up some money to buy a new smartphone, so he babysits on the weekends. There is a proportional relationship between the time Sean spends babysitting (in hours), $x$ , and the amount of money he earns babysitting (in dollars), $y$ . $\newline$ For $1$ hour of babysitting, Sean earns $\$6$ . 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

Sean wants to save up some money to buy a new smartphone, so he babysits on the weekends. There is a proportional relationship between the time Sean spends babysitting (in hours),

x

, and the amount of money he earns babysitting (in dollars),

y

.

\newline

For

1

hour of babysitting, Sean earns

\$6

. Write the equation for the relationship between

x

and

y

.

\newline

y =

____

Identify Given Values: Step $1$ : Identify the given values from the problem description. $\newline$ Sean earns $\$6$ for $1$ hour of babysitting. So, $x = 1$ hour and $y = \$6$ .
Calculate Constant of Proportionality: Step $2$ : Calculate the constant of proportionality, $k$ . $k = \frac{y}{x} = \frac{6}{1} = 6$ .
Write Proportional Relationship Equation: Step $3$ : Write the equation for the proportional relationship using the constant of proportionality. $\newline$ The equation is $y = kx$ , so substituting $k = 6$ , we get $y = 6x$ .

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