Question

the graph represents the number of haircuts, y, a hair stylist can give over time, x. use the graph to find the constant of proportionality and write an equation.

the constant of proportionality is dropdown
the equation that represents the number of haircuts the stylist can give in an hour is dropdown

Explanation:

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"concepts_used": [
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"Proportional Relationship Equation",
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"current_concepts": [
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</pre_analysis>

<reasoning>

Identify points on the graph

Using the Graphing Proportional Relationships knowledge point
\[
(x, y) \in \{(2, 1), (4, 2), (6, 3)\}
\]

Calculate the constant of proportionality

Using the Constant of Proportionality knowledge point
\[
k = \frac{y}{x} = \frac{1}{2} = 0.5
\]

Write the proportional equation

Using the Proportional Relationship Equation knowledge point
\[
y = kx \implies y = \frac{1}{2}x
\]
</reasoning>

<answer>
The graph represents the number of haircuts, \(y\), a hair stylist can give over time, \(x\). Use the graph to find the constant of proportionality and write an equation.

The constant of proportionality is <blank>\(\frac{1}{2}\)</blank>
The equation that represents the number of haircuts the stylist can give in an hour is <blank>\(y = \frac{1}{2}x\)</blank>
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Constant of Proportionality"
]
}
</post_analysis>

Answer:

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<reasoning>

Identify points on the graph

Using the Graphing Proportional Relationships knowledge point
\[
(x, y) \in \{(2, 1), (4, 2), (6, 3)\}
\]

Calculate the constant of proportionality

Using the Constant of Proportionality knowledge point
\[
k = \frac{y}{x} = \frac{1}{2} = 0.5
\]

Write the proportional equation

Using the Proportional Relationship Equation knowledge point
\[
y = kx \implies y = \frac{1}{2}x
\]
</reasoning>

<answer>
The graph represents the number of haircuts, \(y\), a hair stylist can give over time, \(x\). Use the graph to find the constant of proportionality and write an equation.

The constant of proportionality is <blank>\(\frac{1}{2}\)</blank>
The equation that represents the number of haircuts the stylist can give in an hour is <blank>\(y = \frac{1}{2}x\)</blank>
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Constant of Proportionality"
]
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</post_analysis>