Question

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

Answer 1

To transform the equation \( 4x - 8y = 24 \) into slope-intercept form, we need to isolate \( y \) on one side of the equation. The slope-intercept form is given by \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Here are the steps to rearrange the equation:

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 the fractions:
\[
y = \frac{1}{2}x - 3
\]

Now the equation is in the slope-intercept form \( y = mx + b \).

Thus, the final answer is:
\[
y = \frac{1}{2}x - 3
\]