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

−8y=−4x+24
negative 8 y equals negative 4 x plus 24

4x−8y−24=0
4 x minus 8 y minus 24 equals 0

y=12x−3

Answer 1

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

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

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

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

Looking at your options, it seems they don’t match this correctly. If the options were:

1. \(4x - 8y = 24\)
2. \(-8y = -4x + 24\)
3. \(4x - 8y - 24 = 0\)
4. \(y = 12x - 3\)

The second option, \(-8y = -4x + 24\), is the closest correct transformation before reaching slope-intercept form.

Therefore, the slope-intercept form based on the calculations is \( y = \frac{1}{2}x - 3\), and that is not listed in your provided responses.