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

Question

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 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 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 4, and the y-intercept is (0, 12).
The slope is 4, and the y-intercept is left parenthesis 0 comma 12 right parenthesis .

Answer 1

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

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

2. Isolate \( y \): \[ -3y = -4x + 12 \] \[ y = \frac{4}{3}x - 4 \]

From this equation, we can see that:

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

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