Lines are parallel when their slopes are the same.

First, we need to place the given equation in the slope-intercept form.

Subtract from both sides of the equation.

Simplify.

Divide both sides of the equation by .

Simplify.

Reduce.

Because the given line has the slope of , the line parallel to it must also have the same slope.

Parallel lines have the same slope and different y-intercepts. If their y-intercepts and slopes are the same they are the same line, and therefore not parallel. Thus the only one that fits the description is:

Parallel lines have the same slope and different y-intercepts. If their y-intercepts and slopes are the same they are the same line, and therefore not parallel. Thus the only one that fits the description is:

Lines are parallel when their slopes are the same.

First, we need to place the given equation in the slope-intercept form.

Subtract from both sides of the equation.

Simplify.

Divide both sides of the equation by .

Simplify.

Reduce.

Because the given line has the slope of , the line parallel to it must also have the same slope.

Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.

3x + 4y = 12

4y = _–_3x + 12

y = –(3/4)x + 3

slope = _–_3/4

We know that the second line will also have a slope of _–_3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

2 = _–_3/4(1) + b

2 = _–_3/4 + b

b = 2 + 3/4 = 2.75

Plug the y-intercept back into the equation to get our final answer.

y = –(3/4)x + 2.75

Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.

3x + 4y = 12

4y = _–_3x + 12

y = –(3/4)x + 3

slope = _–_3/4

We know that the second line will also have a slope of _–_3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

2 = _–_3/4(1) + b

2 = _–_3/4 + b

b = 2 + 3/4 = 2.75

Plug the y-intercept back into the equation to get our final answer.

y = –(3/4)x + 2.75

Parallel lines have the same slope and differing y-intercepts. Since is the only equation with the same slope, and the y-intercept is different, this is the equation of the parallel line.

We are told at the beginning of this problem that line is described by . Since is our slope-intecept form, we can see that for this line. Since parallel lines have equal slopes, we must determine if line has a slope of .

Since we know that passes through points and , we can apply our slope formula:

Thus, the slope of line is 1. As the two lines do not have equal slopes, the lines are not parallel.

We are told at the beginning of this problem that line is described by . Since is our slope-intecept form, we can see that for this line. Since parallel lines have equal slopes, we must determine if line has a slope of .

Since we know that passes through points and , we can apply our slope formula:

Thus, the slope of line is 1. As the two lines do not have equal slopes, the lines are not parallel.

Parallel lines have the same slope and differing y-intercepts. Since is the only equation with the same slope, and the y-intercept is different, this is the equation of the parallel line.