Identify the slope and the y -intercept of the equation 4x−3y=12 .(1 point)ResponsesThe 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).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).

1 answer

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

Starting with the original equation:

  1. Rearrange the equation to solve for \( y \): \[ -3y = -4x + 12 \] \[ y = \frac{4}{3}x - 4 \]

Now we can see that the equation is in the form \( y = mx + b \).

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

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

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