Question

the value of y varies directly with x, and y = 40 when x = 8.

what is y when x = 7?

y = ?

remember: y = kx

Explanation:

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"concepts_used": [
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"new_concepts": [
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<reasoning>

Set up the direct variation equation

Using the Linear Equations knowledge point, we start with the direct variation formula:
\[y = kx\]
where \(k\) is the constant of variation.

Solve for the constant of variation k

Using the One-Step Equations knowledge point, we substitute the given values \(y = 40\) and \(x = 8\) into the equation to find \(k\):
\[40 = k \cdot 8\]
\[k = \frac{40}{8} = 5\]

Calculate the value of y when x is 7

Now we use our determined constant \(k = 5\) and substitute \(x = 7\) back into the variation equation:
\[y = 5 \cdot 7\]
\[y = 35\]
</reasoning>

<answer>
The value of y varies directly with x, and y = 40 when x = 8.

What is y when x = 7?

y = <blank>35</blank>
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Direct Variation"
]
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</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Set up the direct variation equation

Using the Linear Equations knowledge point, we start with the direct variation formula:
\[y = kx\]
where \(k\) is the constant of variation.

Solve for the constant of variation k

Using the One-Step Equations knowledge point, we substitute the given values \(y = 40\) and \(x = 8\) into the equation to find \(k\):
\[40 = k \cdot 8\]
\[k = \frac{40}{8} = 5\]

Calculate the value of y when x is 7

Now we use our determined constant \(k = 5\) and substitute \(x = 7\) back into the variation equation:
\[y = 5 \cdot 7\]
\[y = 35\]
</reasoning>

<answer>
The value of y varies directly with x, and y = 40 when x = 8.

What is y when x = 7?

y = <blank>35</blank>
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Direct Variation"
]
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