Question

Transform the linear equation 4x - 8y = 24 to slope-intercept form. 4x - 8y - 24 = 0; y = 1/2 * x - 3; - 8y = - 4x + 24; 4x - 8y = 24

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. Move the \( 4x \) term to the right side of the equation:
\[
-8y = -4x + 24
\]

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

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

So, the slope-intercept form of the equation \( 4x - 8y = 24 \) is:
\[
y = \frac{1}{2}x - 3
\]