Identify the slope and the y

Question

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

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

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

The slope is 43
4
3
, and the y-intercept is (0, −4)
(
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
−
4
3
, and the y-intercept is (0, 4)
(
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
4
3
, and the y-intercept is (0, 4)
(
0
,

4
)
.

Answer 1

To find the slope and the 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.

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

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

From this equation, we can see that:

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

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

Answer 2

Transform the linear equation −2y=14−6x to slope-intercept form.

Answer 3

To transform the linear equation \(-2y = 14 - 6x\) into slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), follow these steps:

1. Start with the equation: \[ -2y = 14 - 6x \]

2. To isolate \(y\), divide every term on both sides by \(-2\): \[ y = \frac{14}{-2} - \frac{6x}{-2} \]

3. Simplify the fractions: \[ y = -7 + 3x \]

4. Rearranging the equation gives: \[ y = 3x - 7 \]

Now, the equation is in slope-intercept form \(y = mx + b\) where:

• The slope \(m\) is \(3\).
• The y-intercept \(b\) is \(-7\).

Thus, the slope-intercept form of the equation is: \[ y = 3x - 7 \]