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 = 0 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}.
Describe what it means for two lines to be perpendicular.
If two lines are perpendicular, state the product of their gradients.
State whether the following pairs of lines are perpendicular:
y = x + 1 and y = x - 1
y = 3 x - 7 and y = - 3 x + 6
y = - 3 x + 6 and y = \dfrac{x}{3} + 7
y = \dfrac{2 x}{3} + 4 and y = -1 - \dfrac{3 x}{2}
y = - \dfrac{x}{3} - 9 and y = - \left( 3 x - 27 \right)
y = 3 x - 5 and y = -\dfrac{1}{3} x + 6
y=-\dfrac{2x}{3}+1 and y=-1+\dfrac{3x}{2}
y=\dfrac{3x}{5}+6 and y=\dfrac{-5x-30}{-3}
Given that the following pairs of lines are perpendicular, calculate the value of m:
5 x + 4 y + 8=0 \\m x + 9 y - 8=0
- 6 x + 6 y - 8=0 \\ m x + 10 y + 8=0
Find the gradient of the line perpendicular to the following lines:
Line with gradient 6
Consider the lines L_{1}: 8 x = - 7 y + 3 and L_2: 7 y - 8 x - 7 = 0.
Find the gradient of line L_{1}.
Find the gradient of line L_{2}.
Are the two lines perpendicular?
Find the equation of a line described by the following information:
Perpendicular to the x-axis and passes through \left( - 8 , - 1 \right).
Perpendicular to the y-axis and passes through \left( - 8 , - 8 \right).
Perpendicular to y = - \dfrac{x}{2} + 5, and goes through the point \left(0, 6\right).
Perpendicular to y = 6 x + 10, and has the same y-intercept.
Perpendicular to the line that passes through \left(1, 1\right) and \left(3, 13\right), and has a y-intercept of \left(0, - 4 \right).
The line L_{1} is perpendicular to y = 5 x - 4 and cuts the y-axis at 1.
Find the gradient of line L_{1}.
Find the equation of line L_{1}.
The line L_{1} is perpendicular to y = 10 x + 8 and passes through the point of intersection of the lines y = x + 5 and 8 x - 10 y + 60 = 0.
Find the gradient of line L_{1}.
Find the point of intersection of y = x + 5 and 8 x - 10 y + 60 = 0.
Find the equation of the perpendicular line L_{1}.