Question

Write 3x−8y=12
in slope-intercept form.

Answer 1

To convert the equation \(3x - 8y = 12\) 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:
\[
3x - 8y = 12
\]

2. Isolate the term with \(y\) on one side. To do this, subtract \(3x\) from both sides:
\[
-8y = -3x + 12
\]

3. Next, divide every term by \(-8\) to solve for \(y\):
\[
y = \frac{-3x}{-8} + \frac{12}{-8}
\]

4. This simplifies to:
\[
y = \frac{3}{8}x - \frac{3}{2}
\]

Thus, the equation in slope-intercept form is:
\[
y = \frac{3}{8}x - \frac{3}{2}
\]