Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Qn A:
Parallel lines have the same gradient so gradient of line is 3.
Eqn of line: y = 3x + c
Since line passes through (1,4), subt coordinates into the equation to find c.
4 = 3(1) + c
c = 1
Hence, equation of the line is y = 3x + 1.
Qn B:
The product of the gradient of perpendicular lines is -1.
M₁ x M₂ = -1
To find the gradient of one perpendicular line,
M₂ = -1 ÷ M₁
Gradient of line = 3 ÷ (-1) = -3
Eqn of line: y = -3x + c
Since line passes through (-3,-1), subt coordinates into the equation to find c
-1 = -3(-3) + c
c = -10
Hence, equation of line is y = -3x - 10.
Qn C:
Rearrange the equation to y = mx + c form.
3y = x - 12
y = 1/3x - 4
Parallel lines have the same gradient so gradient of line is 1/3.
Eqn of line: y = 1/3x + c
Since line passes through (18,2), subt coordinates into the equation to find c
2 = 1/3(18) + c
c = -4
Hence, equation of line is y = 1/3x - 4.
Qn D:
Rearrange the equation to y = mx + c form.
2y + 6 = 3x
2y = 3x - 6
y = 3/2x - 3
Since line is perpendicular to y = 3/2x - 3, gradient of line = -1 ÷ 3/2 = -2/3
Eqn of line: y = -2/3x + c
Since line passes through (3,3), subt coordinates into the equation to find c
3 = -2/3x(3) + c
c = 5
Hence, equation of line is y = -2/3x + 5.