Question

Transform the linear 4x - 8y = 24 to slop intercept form.

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

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

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

Now the equation is in slope-intercept form, \( y = \frac{1}{2}x - 3 \).

Here, the slope \( m \) is \( \frac{1}{2} \) and the y-intercept \( b \) is \(-3\).