Question

the equation \\(y = \frac{1}{5}x\\) represents a proportional relationship. explain how you can tell the relationship is proportional from the graph of the equation, and how you can find the constant of proportionality.

Explanation:

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<reasoning>

Identify proportional graph features

Using the Graphing Proportional Relationships knowledge point
\[

$$\begin{aligned} &\text{Graph is a straight line.}\\ &\text{Graph passes through the origin } (0,0). \end{aligned}$$

\]

Identify the constant of proportionality

Using the Proportional Relationship Equation and Constant of Proportionality knowledge points
\[

$$\begin{aligned} &y = kx \implies y = \frac{1}{5}x\\ &k = \frac{1}{5} \end{aligned}$$

\]
</reasoning>

<answer>
A graph represents a proportional relationship if it is a straight line that passes through the origin \((0,0)\).

For the equation \(y = \frac{1}{5}x\), the constant of proportionality is the coefficient of \(x\), which is \(\frac{1}{5}\).
</answer>

<plot>
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"type": "functiongraph",
"params": [
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"js": "0.2*x",
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"properties": {
"strokeColor": "#8C55F2",
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"name": "y = 1/5 x",
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Answer:

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<reasoning>

Identify proportional graph features

Using the Graphing Proportional Relationships knowledge point
\[

$$\begin{aligned} &\text{Graph is a straight line.}\\ &\text{Graph passes through the origin } (0,0). \end{aligned}$$

\]

Identify the constant of proportionality

Using the Proportional Relationship Equation and Constant of Proportionality knowledge points
\[

$$\begin{aligned} &y = kx \implies y = \frac{1}{5}x\\ &k = \frac{1}{5} \end{aligned}$$

\]
</reasoning>

<answer>
A graph represents a proportional relationship if it is a straight line that passes through the origin \((0,0)\).

For the equation \(y = \frac{1}{5}x\), the constant of proportionality is the coefficient of \(x\), which is \(\frac{1}{5}\).
</answer>

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