Transform the linear equation 4x−8y=24

Question

to slope-intercept form.(1 point)
Responses

4x−8y=24

4 x minus 8 y equals 24
4x−8y−24=0
4 x minus 8 y minus 24 equals 0
−8y=−4x+24
negative 8 y equals negative 4 x plus 24
y=12x−3

Answer 1

To transform the equation \(4x - 8y = 24\) to 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. Subtract \(4x\) from both sides: \[ -8y = -4x + 24 \]

3. Divide every term by \(-8\) to solve for \(y\): \[ y = \frac{4}{8}x - \frac{24}{8} \]

4. Simplify: \[ y = \frac{1}{2}x - 3 \]

So, the slope-intercept form is: \[ y = \frac{1}{2}x - 3 \]

None of the options exactly match our result, but the transformation steps are correct. The slope is \(\frac{1}{2}\) and the y-intercept is \(-3\).