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)
Slope is 4; y- intercept is (0, 12)
Question 6
7. Write y − 6x = 5 in slope-intercept form.(1 point)
y =

Answer 1

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

Starting with the equation:

\[ 4x - 3y = 12 \]

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

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

2. Divide everything by \(-3\):

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

From this, we can identify the slope \(m\) and y-intercept \(b\):
- The slope \( m = \frac{4}{3} \)
- The y-intercept \( b = -4\) (or the point \( (0, -4) \))

So the correct answer to the slope and y-intercept of the given equation \(4x - 3y = 12\) is:

**Slope is \( \frac{4}{3} \); y-intercept is (0, -4)**.

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Now, to rewrite the equation \(y - 6x = 5\) in slope-intercept form:

Starting with the given equation:

\[ y - 6x = 5 \]

1. Add \(6x\) to both sides:

\[ y = 6x + 5 \]

Now, this equation is in slope-intercept form where:
- The slope \(m = 6\)
- The y-intercept \(b = 5\)

So the answer in slope-intercept form is:

**y = 6x + 5**.