Question

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

A). The slope is 4 over 3, and the y-intercept is (0, −4).

B). The slope is 4 over 3, and the y-intercept is (0, 4).

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

Starting with the given equation:

\[
4x - 3y = 12
\]

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

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

2. Divide every term by \(-3\):

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

From this equation, 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 \( (0, -4) \).

Based on this information, the correct answer is:

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