Question

what is the equation of this linear function?

(y = ?x + \square)

Explanation:

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"concepts_used": [
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<reasoning>

Identify the y-intercept from the graph

Using the Coordinate Plane knowledge point
\[
(x_1, y_1) = (0, -1) \implies b = -1
\]

Calculate the slope of the line

Using the Slope Calculation knowledge point
\[

$$\begin{aligned} &(x_1, y_1) = (0, -1),\quad (x_2, y_2) = (1, -5)\\ &m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-1)}{1 - 0} = -4 \end{aligned}$$

\]

Write the linear equation

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y = mx + b\\ &y = -4x - 1 \end{aligned}$$

\]
</reasoning>

<answer>
What is the equation of this linear function?
\(y =\) <blank>\(-4\)</blank>\(x +\) <blank>\(-1\)</blank>
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Slope-Intercept Form"
]
}
</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Identify the y-intercept from the graph

Using the Coordinate Plane knowledge point
\[
(x_1, y_1) = (0, -1) \implies b = -1
\]

Calculate the slope of the line

Using the Slope Calculation knowledge point
\[

$$\begin{aligned} &(x_1, y_1) = (0, -1),\quad (x_2, y_2) = (1, -5)\\ &m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-1)}{1 - 0} = -4 \end{aligned}$$

\]

Write the linear equation

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y = mx + b\\ &y = -4x - 1 \end{aligned}$$

\]
</reasoning>

<answer>
What is the equation of this linear function?
\(y =\) <blank>\(-4\)</blank>\(x +\) <blank>\(-1\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Slope-Intercept Form"
]
}
</post_analysis>