Math / Data & Statistics

QuestionRon loves to play the piano but doesn't like practicing the exercises his piano teacher assigns. Ron knows the exercises will help him play better though, so he tries to motivate himself using his favorite treat-chocolate chip cookies.
This table shows the relationship between the amount of time (in hours) that Ron practices the piano, $x$ , and how many cookies he gives himself, $y$ . \begin{tabular}{|c|c|} \hline $x$ (hours) & $y$ (cookies) \\ \hline 3 & 9 \\ \hline 4 & 12 \\ \hline 7 & 21 \\ \hline 8 & 24 \\ \hline \end{tabular}
According to the values in the table, do $x$ and $y$ have a proportional relationship? yes no Write an equation for the relationship between $x$ and $y$ . Simplify any fractions. $y=$ $\square$
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Studdy Solution

STEP 1

1. The relationship between $x$ (hours) and $y$ (cookies) is linear.
2. A proportional relationship means $y = kx$ for some constant $k$ .

STEP 2

1. Determine if the relationship is proportional.
2. Find the constant of proportionality $k$ .
3. Write the equation for the relationship.

STEP 3

Check if the ratio $\frac{y}{x}$ is constant for all data points.
For $x = 3, y = 9$ : $\frac{y}{x} = \frac{9}{3} = 3$
For $x = 4, y = 12$ : $\frac{y}{x} = \frac{12}{4} = 3$
For $x = 7, y = 21$ : $\frac{y}{x} = \frac{21}{7} = 3$
For $x = 8, y = 24$ : $\frac{y}{x} = \frac{24}{8} = 3$
Since the ratio $\frac{y}{x}$ is constant, $x$ and $y$ have a proportional relationship.

STEP 4

The constant of proportionality $k$ is 3, since $\frac{y}{x} = 3$ .

STEP 5

Write the equation for the relationship:
$y = 3x$
The equation for the relationship is:
$y = 3x$

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