FINDING EQUATIONS OF PARALLEL AND PERPENDICULAR LINES WORKSHEET

1)  Parallel to y = 3x + 5 and passing through (0, 2)

Solution

2)  Parallel to y = 4x - 1 and passing through (0, 6)

Solution

3)  Parallel to y = 5x and passing through (0, -3)

Solution

4) Parallel to y = -2x + 10 and passing through the origin

Solution

5) Parallel to x + y = 8 and passing through (0, -4)

Solution

6)  Parallel to x - 2y + 3 = 0 and passing through (0, 5)

Solution

7)  Write down equation of the line parallel to line 1 and passes through A.

Solution

8)  Write down equation of the line parallel to line 1 and passes through A.

Solution

9)  Write down equation of the line parallel to line 1 and passes through A.

1)  Perpendicular to y = 2x + 4 and passing through (0, 3)

Solution

2)  Perpendicular to y = -3x - 8 and passing through (0, -2)

Solution

3)  Perpendicular to x + y = 6 and passing through (0, 1)

Solution

4)  Perpendicular to y = (1/3)x - 2 and passing through the origin            Solution

5)  Perpendicular to y = (-1/5)x + 8 and passing through (0, -2)                   Solution

6)  Perpendicular to y = (-2/9)x - 10 and passing through (0, 6)                    Solution

7) Line A passes through the points (3, 6) and (5, -2) Line B passes through the points (2, 5) and (8, k) Line A and Line B are parallel. Find the value of k.

• Line A passes through the points (-3, -1) and (-1, 9)
• Line B passes through the points (-2, 1) and (k, 4)
• Line A and Line B are perpendicular. Find the value of k.

1)  A straight line passes through the points

A(1, 4) and B(5, 16)

a) Find the equation of the line parallel to AB that passes through (1, 7)

b)  Find the equation of the line perpendicular to AB that passes through the midpoint of AB.

Solution

2)  Are the lines 2x + y = 8 and y = 2x + 5 parallel?

Solution

3)  Are the lines 4x - y - 5 = 0 and x + 4y + 1 = 0 perpendicular?                       Solution

4)  The Line L has equation y = 2x + 8.

The line L crosses the x-axis at the point A.

The line M is perpendicular to Line L and passes through the point A

a) Find the coordinates of the point A.

b) Find equation of the line M.                     Solution

5)  The point A has coordinates (-12, -7) and the point B has coordinates (-8, 1). Find the equation of the line parallel to AB and passing through (2, 5)

Solution

6)  The point A has coordinates (-12, -7) and the point B has coordinates (-8, 1). Find the equation of the line parallel to AB and passing through (2, 5)

Solution

Tell whether the lines are parallel, perpendicular, or neither.

Problem 1 :

Line 1 : through (-3, -7) and (1, 9)

Line 2 : through (-1, -4) and (0, -2)

Solution

Problem 2 :

Line 1 : through (2, 7) and (-1, -2)

Line 2 : through (3, -6) and (-6, -3)

Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.

Solution

Problem 3 :

y = 3x + 4

y = 3x + 7

Solution

Problem 4 :

y = -4x + 1

4y = x + 3

Solution

Problem 5 :

y = 2x - 5

y = 5x - 5

Solution

Problem 6 :

y = -1/3x + 2

y = 3x - 5

Solution

Problem 7 :

y = 3/5x - 3

5y = 3x - 10

Solution

Problem 8 :

y = 4

4y = 6

Solution

Problem 9 :

The line Q passes through the points (−10, −2) and (−8, −8) The line R passes through the points (1, 2) and (10, a) The lines Q and R are perpendicular. Find the value of a.

Solution

Problem 10 :

The point C has coordinates (2, −3) and the point D has coordinates (4, 6). Find the equation of the line perpendicular to CD and passing through D.

Solution