11.16 Parallel lines
The equations y = 2 x, y = 2 x + 5 and \\y = 2 x - 7 have been graphed on the same number plane:
What do all of the equations have in common?
What do all the lines have in common?
State whether the following pairs of lines are parallel:
y = - 3 x - 2 and y = - 3 x + 9
y = - 2 x - 5 and y = - 2 x - 8
y = 7 x + 8 and y = - 5 x + 8
y = 4 x-1 and y = 4 x - 6
x=4 and y = 5
y = 7 x - 5 and y = - 7 x + 6
y = 3 x - 5 and y = -\dfrac{1}{3} x + 6
y=-8x-2 and 9x+7
State whether the following lines are parallel to y = 7 x + 3:
y = 7 x - 3
y = 6 x + 3
y = 7 x + 4
y = 7 x
y = 6 x + 4
y = - 7 x + 3
y = 3x + 7
y = - 3 x - 7
State whether the following lines are parallel to y = - 3 x + 2:
y = 3 x
- 3 y - x = 5
y = - 10 - 3 x
y + 3 x = 7
State whether the following lines are parallel to y = 9 x + 2:
y = 9 x
y = -9 x + 5
y = - 9 x + 2
y = 9 x - 2
Consider the lines L_{1}: 5 x + 8 y = 10 and L_{2}: y = - \dfrac{5 x}{8} + 8.
Find the gradient of line L_{1}.
Find the gradient of line L_{2}.
Are the two lines parallel?
Consider the line y = 2 x + 2. If every point on the line is shifted 2 units up, find the equation of the new line.
Every point on a particular line is shifted 6 units down. The resulting line has equation \\ y = 2 x - 2. Find the equation of the original line.
Find the equation of a line described by the following information:
Parallel to the x-axis and passes through \left( - 10 , 2\right).
Parallel to the y-axis and passes through \left( - 7 , 2\right).
Parallel to the line y = - 3 x - 8 and cuts the y-axis at - 4.
Parallel to the line y = 8 x - 3 and cuts the y-axis at 5.
Parallel to the line y = - 2 x + 9 and passes through the point \left( - 3 , 1\right).
If the following pairs of lines are parallel, find the value of b:
y=b x + 4 \\ 2y=\dfrac{4}{5} x - 7
The line L_{1} goes through \left(3, 2\right) and \left( - 2 , 4\right).
Find the gradient of line L_{1}.
Find the equation of the line that has a y-intercept of 1 and is parallel to line L_{1}.
The line L_{1} goes through \left( - 9 , 10\right) and \left(2, - 1 \right).
Find the gradient of line L_{1}.
Find the equation of the line that passes through \left(10, 8\right) and is parallel to line L_{1}.
The line L_{1} passes through the point \left(9, - 5 \right) and is parallel to the line y = - 5 x + 2.
Find the gradient of line L_{1}.
Find the equation of line L_{1}.
Consider the following points on the number plane:
Point A \left(2, - 1 \right)
Point B \left(4, - 7 \right)
Point C \left( - 3 , 1\right)
Point D \left( - 6 , 10\right)
Find the gradient of the line AB.
Find the gradient of the line CD.
Is the line CD parallel to AB?
Consider the following points on the number plane:
Point P \left(0, - 1 \right)
Point Q \left(5, 0\right)
Point R \left(0, 6\right)
Point S \left( - 5 , 5\right)
Find the gradient of PQ.
Find the gradient of RS.
Are PQ and RS parallel?
Are QR and PS parallel?
Determine whether the following sets of points are collinear:
Point A \left( - 4 , 3\right), Point B \left( - 2 , 7\right) and Point C \left( - 7 , - 3 \right).
Point A \left( - 3 , 1\right), Point B \left( - 2 , 6\right) and Point C \left(0, 14\right).
Point A \left( - 2 , 4\right), Point B \left( 2 , 2 \right) and Point C \left( 4 , 1\right).