Question

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

options:

A). The slope is 43, and the y-intercept is (0, −4).

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

C). The slope is −43, and the y-intercept is (0, 4).

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

Answer 1

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

Starting with the equation:

\[
4x - 3y = 12
\]

We will isolate \( y \):

1. Subtract \( 4x \) from both sides:
\[
-3y = -4x + 12
\]

2. Divide every term by \(-3\):
\[
y = \frac{4}{3}x - 4
\]

From the slope-intercept form \( y = mx + b \), we can see that:

- The slope \( m = \frac{4}{3} \).
- The y-intercept \( b = -4 \), which corresponds to the point (0, -4).

Thus, the correct option is:

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