Slope-Intercept Form Quick Check

Question

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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

Answer 1

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 = \(\frac{1}{2}x - 3\).