Question

if a line has an x-intercept at (x = -6) and a y-intercept at (y = -9), find its equation in the form (y = mx + b).

(y =)

Explanation:

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<reasoning>

Identify the given intercepts as coordinate points

The x-intercept is at \(x = -6\), which corresponds to the point \((-6, 0)\).
The y-intercept is at \(y = -9\), which corresponds to the point \((0, -9)\).

Calculate the slope of the line

Using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\):
\[
m = \frac{-9 - 0}{0 - (-6)} = \frac{-9}{6} = -\frac{3}{2}
\]

Write the equation in slope-intercept form

The slope-intercept form is \(y = mx + b\), where \(b\) is the y-intercept (\(b = -9\)):
\[
y = -\frac{3}{2}x - 9
\]
</reasoning>

<answer>
If a line has an x-intercept at \(x = -6\) and a y-intercept at \(y = -9\), find its equation in the form \(y = mx + b\).

\(y =\) <blank>\(-\frac{3}{2}x - 9\)</blank>
</answer>

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

Answer:

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"step_cot",
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"Slope-Intercept Form",
"Line Intercepts"
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"Linear Equations"
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}
</pre_analysis>

<reasoning>

Identify the given intercepts as coordinate points

The x-intercept is at \(x = -6\), which corresponds to the point \((-6, 0)\).
The y-intercept is at \(y = -9\), which corresponds to the point \((0, -9)\).

Calculate the slope of the line

Using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\):
\[
m = \frac{-9 - 0}{0 - (-6)} = \frac{-9}{6} = -\frac{3}{2}
\]

Write the equation in slope-intercept form

The slope-intercept form is \(y = mx + b\), where \(b\) is the y-intercept (\(b = -9\)):
\[
y = -\frac{3}{2}x - 9
\]
</reasoning>

<answer>
If a line has an x-intercept at \(x = -6\) and a y-intercept at \(y = -9\), find its equation in the form \(y = mx + b\).

\(y =\) <blank>\(-\frac{3}{2}x - 9\)</blank>
</answer>

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