Which equation represents a line that is parallel to the line whose equation is 2x+3y = 12

1. 6y-4x=2
2. 6y + 4x =2
3. 4x-6y = 2

To determine the equation of a line that is parallel to another line, we need to consider that parallel lines have the same slope.

The given line has the equation 2x+3y = 12. To find the slope of this line, we need to rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope.

Rearranging the equation:

2x + 3y = 12
3y = -2x + 12
y = (-2/3)x + 4/3

From this equation, we can see that the slope is -2/3.

Now let's analyze the answer choices:

1. 6y - 4x = 2:
To find the slope, we need to rearrange the equation to solve for y:
6y = 4x + 2
y = (4/6)x + 2/6
y = (2/3)x + 1/3

The slope of this equation is 2/3, which is not equal to the slope of the given line (-2/3). Hence, this equation is not parallel to the given line.

2. 6y + 4x = 2:
Rearranging the equation to solve for y:
6y = -4x + 2
y = (-4/6)x + 1/3
y = (-2/3)x + 1/3

The slope of this equation is -2/3, which is equal to the slope of the given line (-2/3). Hence, this equation is parallel to the given line.

3. 4x - 6y = 2:
Rearranging the equation to solve for y:
-6y = -4x + 2
y = (4/6)x - 1/3
y = (2/3)x - 1/3

The slope of this equation is 2/3, which is not equal to the slope of the given line (-2/3). Hence, this equation is not parallel to the given line.

Therefore, the equation that represents a line parallel to the line 2x + 3y = 12 is option 2: 6y + 4x = 2.

To find an equation that represents a line parallel to the given line, we need to have the same slope.

The given equation is 2x + 3y = 12.

To determine the slope of this line, we need to solve the equation for y in terms of x.

Rearranging the equation, we have:
3y = -2x + 12
y = (-2/3)x + 4

From the equation y = (-2/3)x + 4, we can see that the slope is -2/3.

To find an equation for a line parallel to this, we need to choose an equation with the same slope.

Out of the given options, the equation that has the same slope is:
2. 6y + 4x = 2

Therefore, the equation that represents a line parallel to the line 2x + 3y = 12 is 6y + 4x = 2.

compare their slopes

For Ax + By = C
the slope = -A/B
( you can do the calculation in your head)

slope of given line = -2/3
slope of first choice = 6/4 = 3/2 , nope
etc