Question

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

The slope is 43/, and the y-intercept is (0, 4)


The slope is 4/3, and the y-intercept is (0, −4)


The slope is 4, and the y-intercept is (0, 12).

The slope is −4/3, and the y-intercept is (0, 4)

Answer 1

To find the slope and the y-intercept of the equation \(4x - 3y = 12\), we first need to rewrite it in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the equation:

\[
4x - 3y = 12
\]

Now, solve for \(y\):

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

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

2. Divide by \(-3\):

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

From this form, we can see that:

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

Thus, the y-intercept in coordinate form is (0, -4).

The correct response is:

**The slope is \( \frac{4}{3} \), and the y-intercept is (0, −4).**