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Straight LinesStraight Lines
Objectives:B Grade Explore the gradients of parallel straight line
graphs
A Grade Explore the gradients of perpendicular straight line graphs
Prior knowledge: Recognise the equations of straight line graphs and find the gradients of straight line graphs
Rearrange equations to make a variable the subject
Straight LinesStraight Lines
Find the equation of a line parallel to 2x + y = 4 that crosses they axis at -3
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• First, rearrange the equation in the form y = mx + c
y = -2x + 4• Identify the gradient In this case - 2Any line with the samegradient is parallelThe line that has the samegradient and has a y-intercept of -3 is:
y = -2x - 3
Parallel Lines
Straight LinesStraight Lines
Finding the equations of the lines parallel to the following equationsand that pass through the coordinates given:
1. y = 3x (0,5)2. y = - x (0,2)3. y = 2x + 4 (0,-3)4. y = 3x - 2 (0,-1)
5. y = -4x - 4 (0, 3)6. 2x – y = 2 (0,-7)7. 2y – 6x = 4 (0, -4)8. 2x + 4y = 4 (0, 5)9. y = 2x + 1 (0, 2)10. y = - x - 4 (0, 1)
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y = 3x + 5y = - x + 2y = 2x - 3y = 3x - 1y = - 4x + 3y = 2x - 7y = 3x - 4
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y = - x + 5y = 6x + 2y = - x + 1
Straight LinesStraight LinesPerpendicular Lines
Perpendicular means “at right angles to”
For the line y = xdraw a line that is perpendicular to it.
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y = xy = -x
Notice how the gradientis now negative.
The gradient of a perpendicular line isalways the opposite sign.
Straight LinesStraight Lines
For the line y = 2xdraw a line that is perpendicular to it.
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y = 2x
y = -½x
Straight LinesStraight Lines
For the line y = 3xdraw a line that is perpendicular to it.
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y = 3x
y = - x13
Straight LinesStraight Lines
For the line y = 4xdraw a line that is perpendicular to it.
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y = 4x
y = - x14
Straight LinesStraight Lines
Look at these equations together:
y = xPerpendicular line
y = -x
y = 2x y = -½x
y = 3x y = - x13
y = 4x y = - x14
To summarise:
The gradient of a perpendicular line is the negative reciprocalof the gradient of the original line.
Straight LinesStraight Lines
What is the equation of the line perpendicular to y = 2x + 3 thatgoes 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 5The equation is therefore:
y = -½ x + 5
Straight LinesStraight Lines
Now do these:
y = -x + 15 y = x + 15 y = -x - 15 y = x - 15
