Question

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

The slope is 43

, and the y-intercept is (0, −4)
.
The slope is 4 thirds, and the y-intercept is (0, −4)
. - not selected, this is the correct answer
The slope is 4, and the y-intercept is (0, 12)
.
The slope is 4, and the y-intercept is (0, 12)
. - no response given
The slope is 43
, and the y-intercept is (0, 4)
.
The slope is 4 thirds, and the y-intercept is (0, 4)
. - incorrect
The slope is −43
, and the y-intercept is (0, 4).

Answer 1

To determine 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.

1. Start with the equation:
\[
4x - 3y = 12
\]

2. Solve for \(y\):
\[
-3y = -4x + 12
\]
\[
y = \frac{4}{3}x - 4
\]

From this form, we can see that:
- The slope \(m\) is \(\frac{4}{3}\).
- The y-intercept \(b\) is \(-4\), which means the y-intercept point is \((0, -4)\).

Therefore, the correct response is:
- The slope is \(\frac{4}{3}\), and the y-intercept is \((0, -4)\).