Question

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 negative Start Fraction 4 over 3 End Fraction , and the y-intercept is left parenthesis 0 comma 4 right parenthesis .

The slope is 43
, and the y-intercept is (0, 4)
.
The slope is Start Fraction 4 over 3 End Fraction , and the y-intercept is left parenthesis 0 comma 4 right parenthesis .

The slope is 4, and the y-intercept is (0, 12)
.
The slope is 4, and the y-intercept is left parenthesis 0 comma 12 right parenthesis .

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

Answer 1

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

Starting with the equation:

\[
4x - 3y = 12
\]

We can rearrange the equation to solve for \(y\):

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

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

2. Divide every term 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 \(-4\), which corresponds to the point \((0, -4)\)

Thus, the correct response is:

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