Question

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

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 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 43, and the y-intercept is (0, −4).

1 answer

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

Starting with the given equation:

\[ 4x - 3y = 12 \]

We can isolate \( y \):

  1. Move \( 4x \) to the other side:

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

  1. Divide every term by -3:

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

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 response is:

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