Question

Identify the slope-intercept form and the graph of the line described by the equation. 4x-6y=12

Answer 1

The slope-intercept form of the equation 4x-6y=12 is y=(2/3)x-2. The slope is 2/3 and the y-intercept is -2. The graph of this line is a straight line that slopes upwards and intersects the y-axis at -2.

Step-by-step explanation:

The equation 4x-6y=12 can be rewritten in slope-intercept form y=mx+b as follows:

Subtracting 4x from both sides: -6y = -4x+12
Dividing both sides by -6: y = (4/6)x - 2
Reducing the fraction: y = (2/3)x - 2

In this equation, the slope (m) is 2/3 and the y-intercept (b) is -2.

The slope represents the rate of change of y with respect to x, which means that for every increase of 1 in x, y increases by 2/3. '

The y-intercept is the point where the line intersects the y-axis, which in this case is (0, -2).

So therefore the graph of this line will have a slope of 2/3 and will intersect the y-axis at -2. It will be a straight line that starts below the y-axis (since the y-intercept is negative) and slopes upwards.

Answer 2

So here we have this equation:

`4x-6y=12`

We want to find its slope-intercept form. (y=mx+b)

For this, we just solve the previous equation for y.

`\begin{gathered} 4x-6y=12 \\ 4x-12=6y \\ y=(2)/(3)x-2 \end{gathered}`

Notice that the slope is positive, so the line is going to grow. For this reason, option C is not correct.

If we look at the y-intercept form, we notice that the y-intercept of our line is located at y=-2. So, option D is also incorrect.

And, the point-slope equation of the option A is not correct.

Therefore, the correct option is B.