1. ©G Dear2008 – Not to be sold/Free to use
Stage 4
Year 9
Coordinate
Geometry
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Parallel Lines
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©G Dear2008 – Not to be sold/Free to use

2. Check to see if coefficients of x are equal.
Parallel Lines
Are two lines parallel?
Do they have the same gradient?
m1 = m2
To find out if two lines are parallel put in the form y = mx + b
Check to see if coefficients of x are equal.
GeoGebra

3. Are the two lines parallel?
Parallel Lines
Are the two lines parallel?
10x + 2y - 7 = 0
5x + y - 3 = 0
y - 3 = -5x
2y - 7 = -10x
y = -5x + 3
2y = -10x + 7
y = -5x + 3.5
m1 = -5
m2 = -5
They are parallel !

4. Are the two lines parallel?
Parallel Lines
Are the two lines parallel?
6x + 2y - 3 = 0
3x + y - 3 = 0
y - 3 = -3x
2y - 3 = -6x
y = -3x + 3
2y = -6x + 3
y = -2x + 1.5
m1 = -2
m2 = -3
They are NOT parallel !

5. Are the interval and line parallel?
Parallel Lines
Are the interval and line parallel?
(2,3) to (5,9)
4x + 2y - 6 = 0
y2 – y1
x2 - x1
2y - 6 = -4x
m =
4y = -8x + 6
9 – 3
5 - 2 =
y = -2x + 1.5
m1 = 2
m2 = -2
They are NOT parallel !

6. Are the interval and line parallel?
Parallel Lines
Are the interval and line parallel?
(2,9) to (5,3)
6x + 3y - 5 = 0
y2 – y1
x2-x1
3y - 5 = -6x
m =
4y = -8x + 5
3 – 9
5 - 2 =
y = -2x
m1 = -2
m2 = -2
They are parallel !