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Read the description of a proportional relationship. $\newline$ Jill is thrilled to be cast as Juliet in her school's production of Romeo and Juliet, but she has lot of lines to memorize! There is a proportional relationship between the number of days Jill has been memorizing her lines, $x$ , and the total number of lines she has memorized, $y$ . $\newline$ After $2$ days of practice, Jill has memorized $10$ lines. 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

Jill is thrilled to be cast as Juliet in her school's production of Romeo and Juliet, but she has lot of lines to memorize! There is a proportional relationship between the number of days Jill has been memorizing her lines,

x

, and the total number of lines she has memorized,

y

.

\newline

After

2

days of practice, Jill has memorized

10

lines. 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. $\newline$ Jill has been practicing for $x = 2$ days and has memorized $y = 10$ lines.
Calculate Constant of Proportionality: Step $2$ : Calculate the constant of proportionality, $k$ . Using the formula $k = \frac{y}{x}$ , we find: $k = \frac{10}{2}$ $k = 5$
Write Proportional Relationship Equation: Step $3$ : Write the equation for the proportional relationship using the constant of proportionality. $\newline$ The equation is $y = kx$ . $\newline$ Substituting $k = 5$ , we get: $\newline$ $y = 5x$

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