# Which of the following are equations of parallel lines:x = 3y + 2 3x - 2y = 9 x - y = 7 2x = 2y + 9 3y - 3x + 13 = 0

justaguide | Certified Educator

The slope of parallel lines is the same. Expressing all the lines given in the slope intercept form gives:

y = x/3 - 2

y = 3x/2 - 9/2

y = x - 7

y = x - 9/2

y = x + 13/3

It is seen that the last three lines have a slope of 1 and are parallel to each other.

The parallel lines are x - y = 7, 2x = 2y + 9 and 3y - 3x + 13 = 0

chaobas | Student

"For the line to be parallel, they all must have same slope"

The given equation are as follows

x = 3y + 2------>(1)

3x - 2y = 9------>(2)

x - y = 7------>(3)

2x = 2y + 9------>(4)

3y - 3x + 13 = 0------>(5)

let's convert it into y=mx+c : were m = slope.

x = 3y + 2

3y=x-2

y=1/3 x - 2 : so slope m=1/3

for second equation

3x - 2y = 9

-2y=-3x+9

y = 3/2x -9/2  so slope = 3/2

for the third line

x - y = 7

-y=7-x [multiplying both side by -1]

y=x-7 : so slope is 1

for the 4th line

2x = 2y + 9

2y=2x-9

y=x-(9/2) so the slope is 1

and the fifthe line

3y - 3x + 13 = 0

3y=3x-13

y=x-(13/3) the slope is 1

so we have the line

x - y = 7 :2x = 2y + 9  :3y - 3x + 13 = 0 have same slope which is equal to 1

so these line are parallel

Slopes of parallel lines are same:

y = x/3 - 2

y = 3x/2 - 9/2

y = x - 7

y = x - 9/2

y = x + 13/3

Last 3 have same slope (1) thus they are parallel