Question
Slope-Intercept Form Quick Check
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Question
Transform the linear equation 4x−8y=24
to slope-intercept form.(1 point)
Responses
−8y=−4x+24
negative 8 y equals negative 4 x plus 24
4x−8y=24
4 x minus 8 y equals 24
4x−8y−24=0
4 x minus 8 y minus 24 equals 0
y=1/2x−3
Answers
GPT-4o mini
To transform the equation \(4x - 8y = 24\) into slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), follow these steps:
1. Start with the original equation:
\[
4x - 8y = 24
\]
2. Isolate the term with \(y\) on one side. Begin by moving the \(4x\) to the right side:
\[
-8y = -4x + 24
\]
3. Now, divide each term by \(-8\) to solve for \(y\):
\[
y = \frac{1}{2}x - 3
\]
Hence, the slope-intercept form of the equation is:
\[
y = \frac{1}{2}x - 3
\]
So the correct response is:
**y = \(\frac{1}{2}x - 3\)**.
1. Start with the original equation:
\[
4x - 8y = 24
\]
2. Isolate the term with \(y\) on one side. Begin by moving the \(4x\) to the right side:
\[
-8y = -4x + 24
\]
3. Now, divide each term by \(-8\) to solve for \(y\):
\[
y = \frac{1}{2}x - 3
\]
Hence, the slope-intercept form of the equation is:
\[
y = \frac{1}{2}x - 3
\]
So the correct response is:
**y = \(\frac{1}{2}x - 3\)**.