## Properties of Lines Exercise

1. By finding the gradient of each line, state whether the two lines are parallel, perpendicular or neither.

a. y = 4x − 6 and y − 4x = 9

b. y = x and y = -x + 3

c. 4x − 2y + 3 = 0 and 4x − y + 2 = 0

d. y + x = 10 and y + x = 9

e. 2y = 6x − 4 and y = 3x − 2

f. 2x − 6y = 8 and y + 3x = 4

g. 2y − 3 = 8x and 18x − 4y = -8

2. Find the equations of the lines with the following properties (the formula y − y1m(x − x1) may be useful).
Leave the answer in the form ax + by + c = 0

a. Parallel to the line y = 2x − 3 and passing through the point (3, 4)

b. Parallel to the x-axis and passing through the point (-2, 6)

c. A y-intercept of 5 and parallel to the line y = 2x − 3

d. Perpendicular to the line y = 2x + 6 and passing through the point (1, 2)

e. Parallel to the y-axis and passes through the point (-1, 3)

f. Perpendicular to y = 3(2x − 4) and passing through the point (0, 2)

g. Parallel to the line 3x + 3y − 5 = 0 and passing through the point (4, -4)

3. Investigate whether the following sets of points are collinear:

a. (4, 5), (0, 2) and (-8, -4)

b. (-2, 0), (0, -1) and (4, -3)

c. (-6, 5), (-1, 2) and (4, -2)

d. (10, 1), (0, 0) and (-5, -0.5)

4. Find the values of the variables.

a. Find k if the two lines y = kx + 3 and y − 4x = 2 are parallel.

b. Find p if the two lines 2x + 2y = 5 and px − 2y = 9 are parallel.

c. Find if the three points (5, 2), (3, 6) and (q, 8) are collinear.

d. Find s if the lines y = 2x − 5 and 2y = sx + 3 are perpendicular.