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

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)
.

1 answer

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

Starting with the original equation: \[ 4x - 3y = 12 \]

  1. Subtract \(4x\) from both sides: \[ -3y = -4x + 12 \]

  2. Now, divide each term by \(-3\) to solve for \(y\): \[ y = \frac{4}{3}x - 4 \]

From this equation, we can identify:

  • The slope \(m = \frac{4}{3}\)
  • The y-intercept \(b = -4\), which corresponds to the point \((0, -4)\).

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