Transcript Document

Straight Lines
Objectives:
B Grade
A Grade
Prior knowledge:
Explore the gradients of parallel straight line
graphs
Explore the gradients of perpendicular straight
line graphs
Recognise the equations of straight line graphs
and
find the gradients of straight line graphs
Rearrange equations to make a variable the subject
Parallel Lines
Straight Lines
Find the equation of a line parallel to 2x + y = 4 that crosses the
y
y axis at 3
10
• First, rearrange the
equation in the form
y = mx + c
y = -2x + 4
• Identify the gradient
In this case - 2
-10
Any line with the same
gradient is parallel
The line that has the same
gradient and has a
y-intercept of -3 is:
y = -2x - 3
9
8
7
6
5
4
3
2
1
-9
-8
-7
-6 -5
-4
-3
-2
-1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
x
Straight Lines
Finding the equations of the lines parallel to the following equations
and that pass through the coordinates given:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
y = 3x
y = -x
y = 2x + 4
y = 3x - 2
y = -4x - 4
2x – y = 2
2y – 6x = 4
2x + 4y = 4
1
3 y = 2x + 1
y = -x - 4
(0,5)
(0,2)
(0,-3)
(0,-1)
(0, 3)
(0,-7)
(0, -4)
(0, 5)
(0, 2)
(0, 1)
y = 3x + 5
y = -x + 2
y = 2x - 3
y = 3x - 1
y = - 4x + 3
y = 2x - 7
y = 3x - 4
y = - 12 x + 5
y = 6x + 2
y = -x + 1
Perpendicular Lines
Perpendicular means
“at right angles to”
Straight Lines
y
y = -x
y=x
10
9
8
7
For the line y = x
draw a line that is
perpendicular to it.
Notice how the gradient
is now negative.
6
5
4
3
2
1
-10 -9
-8
-7
-6 -5
-4
-3
-2
-1
0
-1
The gradient of a
perpendicular line is
always the opposite
sign.
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
x
Straight Lines
For the line y = 2x
draw a line that is
perpendicular to it.
y
y = 2x
10
9
8
7
y = -½x
6
5
4
3
2
1
-10 -9
-8
-7
-6 -5
-4
-3
-2
-1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
x
Straight Lines
For the line y = 3x
draw a line that is
perpendicular to it.
y
y = 3x
10
9
8
7
y = -13 x
6
5
4
3
2
1
-10 -9
-8
-7
-6 -5
-4
-3
-2
-1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
x
Straight Lines
For the line y = 4x
draw a line that is
perpendicular to it.
y
y = 4x
10
9
8
7
y = -14 x
6
5
4
3
2
1
-10 -9
-8
-7
-6 -5
-4
-3
-2
-1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
x
Straight Lines
Look at these equations together:
y=x
Perpendicular line
y = -x
y = 2x
y = 3x
y = 4x
y = -½x
y = -13 x
y = -14 x
To summarise:
The gradient of a perpendicular line is the negative reciprocal
of the gradient of the original line.
Straight Lines
What is the equation of the line perpendicular to y = 2x + 3 that
goes through (0,5)
The gradient of this line is 2, so the gradient of the
line perpendicular to it is -½
The line crosses the y-axis (the line x = 0) at (0,5), so the
y-intercept is 5
The equation is therefore:
y = -½ x + 5
Straight Lines
Now do these:
y = -x + 15
y = x + 15
y = -x - 15
y = x - 15