Consider a pair of lines that have gradients m_1 and m_2. State the relationship between the gradients when the lines are:
Parallel
Perpendicular
A line l has a gradient of 5. Find the gradient for a line that is:
Parallel to line l
Perpendicular to line l
Consider the pairs of line gradients, m_1 and m_2. For each pair, determine whether the pair of lines are parallel, perpendicular, or neither.
m_1=3, m_2=3
m_1=-2, m_2=2
m_1=\dfrac{1}{4}, m_2=-4
m_1=-\dfrac{2}{3}, m_2=-\dfrac{2}{3}
m_1=1, m_2=0
m_1=\dfrac{3}{5}, m_2=\dfrac{5}{3}
m_1=\dfrac{4}{3}, m_2=-\dfrac{3}{4}
m_1=1, m_2=-1
Consider the following lines:
- Line 1: \enspace 5 x = 6 y + 5
- Line 2: \enspace -6 y - 5 x + 4 = 0
Find the gradient of Line 1.
Find the gradient of Line 2.
Are the two lines perpendicular?
State whether or not the following pairs of lines are perpendicular:
L_{1}: y = 7 x - 5 and L_{2}: y = - 7 x + 6
L_{1}: y = - 8 x - 3 and L_{2}: y = \dfrac{x}{8} - 2
Determine whether the following lines are perpendicular to y = 4 x + 5:
x + 4 y - 5 = 0
y = \dfrac{x}{4} + 5
y = - 4 x + 5
4 x + 16 y + 160 = 0
The lines y = - 5 m x + 1 and y = - 2 + 4 x are parallel. Find the value of m.
If y = \dfrac{2}{5} x-10 is perpendicular to y= m x - 5, find the value of m.
Find the gradient of the following lines:
A line that is perpendicular to the line with gradient 7
Any line perpendicular to y = 4 x - 9
A line, L_1, passes through the point \left(9, - 2 \right) and is parallel to the line y = - 6 x - 6.
Find the gradient of L_1.
Hence, find the equation of L_1.
The line L_1 is perpendicular to y = 6 x + 5 and cuts the y-axis at 1.
Find the gradient of L_1.
Find the equation of L_1.
Find the equation of the following lines in gradient-intercept form:
A line that is parallel to the x-axis and passes through \left(- 5, 2 \right)
A line that is parallel to the y-axis and passes through \left(- 2, 3\right)
A line that is parallel to the line y = 8 x - 3 and cuts the y-axis at 5
Consider the line L with equation 2 x + 5 y - 5 = 0 and point A\left( - 2 , - 3 \right).
Find the gradient, m, of a line that is perpendicular to L.
Write the equation of the line perpendicular to L that passes through point A. Write your answer in general form.
Find the equation of the line that is parallel to y = \dfrac{2 x}{3} - 8 and passes through \left(8, - 9 \right). Write your answer in general form.
A line passes through A\left( - 2 , 9\right) and B\left( - 4 , - 4 \right):
Find the gradient of the line.
Find the equation of a line that has a y-intercept of - 5 and is parallel to the line through A and B.
A line L is perpendicular to the interval joining B \left(4, 0\right) and C \left(10, - 5 \right).
Find the gradient of line L.
Find the equation of line L if it passes through \left( - 9 , - 7 \right).
Find, in general form, the equation of the line that is perpendicular to y = 10 x + 2 and passes through \left(3, 8\right).
A line is perpendicular to 5 x + 2 y + 3 = 0 and passes through point A\left(5, 5\right).
Find the equation of the line in general form.
Does the point \left(3, \dfrac{21}{5}\right) lie on the line?
Find the equation of a line that has a y-intercept of \left(0, - 3 \right) and is perpendicular to the line that passes through A\left( - 10 , - 7 \right) and B\left( - 9 , - 10 \right).
Consider the following lines:
Identify the pairs of lines that are parallel.
State the type of quadrilateral that is enclosed by the four lines.
-
L_{1}: 2 x - 2 y - 2 = 0
L_{2}: 4 x - 4 y + 4 = 0
L_{3}: y = - 3 x + 3
-
L_{4}: 15 x + 5 y + 3 = 0