## Equation of a Line Exercise

1. Re-arrange the following equations to the form ax + by + c = 0.

a. 3x + 2y = 4
b. y = 4x − 8

c. 2x − 4 = y
d. 3x = 5y +9
e. 6y = 3 − 2x
f. g. 3(1 − 4x) = 9y

2. Re-arrange the following equations to the form y = mx + c and give the gradient of each as a fraction

a. 6x = y + 4
b. 2y = -4x + 3
c. 5x − y = 12
d. 12 = 2(y + 3x)
e. 4x + 5y − 20 = 0
f. 4 = 4x − 7y
g. 3x − 2y = 18

3. Find the angle made by the following lines and the positive direction of the x-axis.

a. 3y = 2x − 6
b. x − 3 + 2y = 0
c. 5 + 2x = 8y

4. Find the equation of the following lines in the form ax + by + c = 0:

a. With gradient 3 and y-intercept 4
b. With gradient and y-intercept -2
c. With gradient -0.5 and y-intecept 0.5

5. Find the equations of the following straight lines:

 a. b. 6. Find the equation of each of the following lines and give answer in the form ax + by + c = 0

a. With gradient 2 and passing through (1, 2)
b. With gradient -3 and passing through (2, 3)
c. With gradient 0.5 and passing through (-1,- 2)
d. With gradient 1 and passing through (0, 0)
e. With gradient 3/4 and passing through (-3, 6)
f. With gradient -2.5 and passing through (3, 0)
g. With gradient 0 and passing through (5, 2)

7. Find the equation of the line passing through the following pairs of points. Leave answer in form ax + by + c = 0

a. (3, 4) and (6, 9)
b. (-1, 5) and (2, -3)
c. (2,- 4) and (5, 10)
d. (-3, -1) and (-2,- 8)
e. (16, 1) and (-6, 10)
f. (0, 4) and (-3, 0)
g. (3, 3) and (-3, -3)