Question

What is the slope and y-intercept of the following equation?

4x - 3y = 12

(1 point)
Responses

Slope is −43
; y- intercept is (0, 4)
Slope is negative 4 thirds ; y- intercept is (0, 4)

Slope is 43
; y- intercept is (0, -4)
Slope is 4 thirds ; y- intercept is (0, -4)

Slope is 43
; y- intercept is (0, 4)
Slope is 4 thirds ; y- intercept is (0, 4)

Slope is 4; y- intercept is (0, 12

Answer 1

To find the slope and 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 original equation:

\[ 4x - 3y = 12 \]

First, isolate \(y\):

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

Divide everything 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 \(-4\), which corresponds to the point \((0, -4)\).

So, the correct answer is:
**Slope is \( \frac{4}{3} \); y-intercept is (0, -4).**