Identify the slope and the y

Question

-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 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)
.

Answer 1

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

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

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

Now, we can identify the slope and the y-intercept:

• 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 \((0, -4)\).

So the correct response is:

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