Identify the slope and the y

Question

-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 it in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. Start with the original equation: \[ 4x - 3y = 12 \]

2. Solve for \( y \): \[ -3y = -4x + 12 \]

   Dividing everything by -3: \[ y = \frac{4}{3}x - 4 \]

Now we can identify the slope and the y-intercept:

• The slope \( m \) is \( \frac{4}{3} \).
• The y-intercept \( b \) is \( -4 \); in coordinates, this is the point \( (0, -4) \).

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