Question
Transform the linear equation 4x−8y=24 to slope-intercept form.
options:
A). −8y = −4x + 24
B). 4x − 8y − 24 = 0
C). 4x−8y=24
D). y = 1 over 2x − 3
options:
A). −8y = −4x + 24
B). 4x − 8y − 24 = 0
C). 4x−8y=24
D). y = 1 over 2x − 3
Answers
GPT-4o mini
To transform the linear equation \(4x - 8y = 24\) into slope-intercept form (\(y = mx + b\)), we need to solve for \(y\).
Starting with the original equation:
\[
4x - 8y = 24
\]
1. Subtract \(4x\) from both sides:
\[
-8y = -4x + 24
\]
2. Now, divide every term by \(-8\) to solve for \(y\):
\[
y = \frac{1}{2}x - 3
\]
The slope-intercept form of the equation is:
\[
y = \frac{1}{2}x - 3
\]
Therefore, the correct answer is:
**D). \(y = \frac{1}{2}x - 3\)**
Starting with the original equation:
\[
4x - 8y = 24
\]
1. Subtract \(4x\) from both sides:
\[
-8y = -4x + 24
\]
2. Now, divide every term by \(-8\) to solve for \(y\):
\[
y = \frac{1}{2}x - 3
\]
The slope-intercept form of the equation is:
\[
y = \frac{1}{2}x - 3
\]
Therefore, the correct answer is:
**D). \(y = \frac{1}{2}x - 3\)**