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Linear Equations and Graphs

Parallel and Perpendicular Lines

T wo lines are parallel if they have the same slope. Parallel lines never intersect. The lines shown below are parallel

Paralles lines of slope m.

The lines y = 4x, y = 4x + 5 and y = 4x - 100 are also parallel as they all have slope 4.

 

Perpendicular lines are lines that intersect at right angles (90 degrees). By using Pythagoras’s Theorem it can be shown that two lines with slopes m1 and m2 are perpendicular if  m1×m2 = -1. (Click here to see details.) Hence the slopes are negative reciprocals. That is m1 = -1/m2.


Parallel lines have equal slopes, m1 = m2. Perpendicular lines have negative reciprocal slopes, m1 = -1/m2.

Exercise 9.

 

Find the slope of the two lines:

Equation
Slope
x + y =
(2 d.p.)
x + y =
(2 d.p.)

 

Click on the correct button below for the two lines above:


             

 

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