Question

Identify the slope and the y-intercept of the equation 4x−3y=12 .

Answer 1

To identify the slope and the y-intercept of the equation \(4x - 3y = 12\), we can rearrange it into slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the original equation:

\[
4x - 3y = 12
\]

We can isolate \(y\):

1. Subtract \(4x\) from both sides:

\[
-3y = -4x + 12
\]

2. Divide every term by \(-3\) to solve for \(y\):

\[
y = \frac{4}{3}x - 4
\]

Now, we can identify the slope and the y-intercept:

- The slope \(m\) is \(\frac{4}{3}\).
- The y-intercept \(b\) is \(-4\).

Thus, the slope is \(\frac{4}{3}\) and the y-intercept is \(-4\).