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 4/3, and the y-intercept is (0, −4)

The slope is 4, and the y-intercept is (0, 12).

The slope is −4/3, and the y-intercept is (0, 4)

1 answer

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

Starting with the equation:

\[ 4x - 3y = 12 \]

Now, solve for \(y\):

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

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

  1. Divide by \(-3\):

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

From this form, we can see that:

  • The slope \(m\) is \(\frac{4}{3}\).
  • The y-intercept \(b\) is \(-4\).

Thus, the y-intercept in coordinate form is (0, -4).

The correct response is:

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