Transform the linear equation 4x−8y=24 to slope-intercept form.(1 point)

Question

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
y equals Start Fraction 1 over 2 End Fraction x minus 3

Answer 1

To transform the equation \(4x - 8y = 24\) to slope-intercept form (which is \(y = mx + b\)), we follow these steps:

1. Start with the original equation: \[ 4x - 8y = 24 \]

2. Rearrange the equation to isolate the term involving \(y\): \[ -8y = -4x + 24 \]

3. Divide every term by \(-8\) to solve for \(y\): \[ y = \frac{-4}{-8}x + \frac{24}{-8} \] Simplifying this gives: \[ y = \frac{1}{2}x - 3 \]

The slope-intercept form of the equation is: \[ y = \frac{1}{2}x - 3 \]

Therefore, the correct response from the options you provided is: y = Start Fraction 1 over 2 End Fraction x minus 3.