Question

convert the following equation into standard form.

(y = -7x + 7)

( ? x + y = \text{___})

standard form: (ax + by = c)

Explanation:

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<reasoning>

Identify the given equation and target form

Using the Linear Equations knowledge point
\[

$$\begin{aligned} &\text{Given equation: } y = -7x + 7\\ &\text{Target standard form: } Ax + By = C \end{aligned}$$

\]

Rearrange terms to isolate variables on one side

Using the Linear Equations knowledge point
\[

$$\begin{aligned} &y = -7x + 7\\ &y + 7x = 7\\ &7x + y = 7 \end{aligned}$$

\]

Match coefficients to fill the blanks

Using the Linear Equations knowledge point
\[

$$\begin{aligned} &[?]x + y = \text{blank}\\ &7x + y = 7\\ &\text{Therefore, } [?] = 7 \text{ and the blank is } 7 \end{aligned}$$

\]
</reasoning>

<answer>
Convert the following equation into standard form.
\(y = -7x + 7\)

<blank>7</blank>\(x + y =\) <blank>7</blank>

Standard Form: \(Ax + By = C\)
</answer>

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"Mathematics",
"Algebra",
"Standard Form of Linear Equations"
]
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</post_analysis>

Answer:

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<reasoning>

Identify the given equation and target form

Using the Linear Equations knowledge point
\[

$$\begin{aligned} &\text{Given equation: } y = -7x + 7\\ &\text{Target standard form: } Ax + By = C \end{aligned}$$

\]

Rearrange terms to isolate variables on one side

Using the Linear Equations knowledge point
\[

$$\begin{aligned} &y = -7x + 7\\ &y + 7x = 7\\ &7x + y = 7 \end{aligned}$$

\]

Match coefficients to fill the blanks

Using the Linear Equations knowledge point
\[

$$\begin{aligned} &[?]x + y = \text{blank}\\ &7x + y = 7\\ &\text{Therefore, } [?] = 7 \text{ and the blank is } 7 \end{aligned}$$

\]
</reasoning>

<answer>
Convert the following equation into standard form.
\(y = -7x + 7\)

<blank>7</blank>\(x + y =\) <blank>7</blank>

Standard Form: \(Ax + By = C\)
</answer>

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"question_type": "Fill-in-the-blank",
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"Mathematics",
"Algebra",
"Standard Form of Linear Equations"
]
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