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Read the description of a proportional relationship. $\newline$ The basketball gym at Darrell's school was built in the $1940$ s and needs a lot of repairs. So, the school is asking families for donations to build a new gym. Darrell convinced some local businesses to match a fraction of the families' donations. There is a proportional relationship between the amount of money a family donates (in dollars), $x$ , and the matching contribution (in dollars) from local businesses, $y$ . $\newline$ When a family donates $\$10$ , the businesses contribute $\$5$ . 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

The basketball gym at Darrell's school was built in the

1940

s and needs a lot of repairs. So, the school is asking families for donations to build a new gym. Darrell convinced some local businesses to match a fraction of the families' donations. There is a proportional relationship between the amount of money a family donates (in dollars),

x

, and the matching contribution (in dollars) from local businesses,

y

.

\newline

When a family donates

\$10

, the businesses contribute

\$5

. 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. $\newline$ Amount of money a family donates, $x = \$(10)$ $\newline$ Matching contribution from businesses, $y = \$(5)$ $\newline$ Calculate the constant of proportionality, $k$ , using the formula $k = \frac{y}{x}$ . $\newline$ $k = \frac{5}{10}$ $\newline$ $k = 0.5$
Calculate Constant of Proportionality: Step $2$ : Use the constant of proportionality to write the equation for the proportional relationship. $\newline$ Since $k = 0.5$ , the equation relating $x$ and $y$ is: $\newline$ $y = kx$ $\newline$ $y = 0.5x$

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