Page 54 - Math Course 2 (Book 2)

Parallel and Perpendicular Lines

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MO. 8 - L4b Step 2 The slope of given line is .So, the
2
slope of the line perpendicular to this
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Identifying Perpendicular Lines line is the opposite reciprocal of , or
2
2
– .
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Key Concept Step 3 Use the point-slope form to find the
equation.

Perpendicular Lines in a Coordination Plane y – y = m(x – x ) Point-slope form
1 1
2
Words Two nonvertical lines are perpendicular y – (–1) = – (x – 4) (x , x ) = (4, –1)
1
1
7
2
if the product of their slopes is –1. That and m = – 7
is, the slopes are opposite reciprocals of 2
each other. Vertical lines and horizontal y + 1 = – (x – 4) Simplify.
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lines are also perpendicular. 2 8
y + 1 = – x + 7 Distributive Property
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Model 1 y 2 8 Subtract 1 from each
m = – 2 y + 1 – 1 = – x + – 1 side.
7
7
2 1
y = – x + Simplify.
7 7
0 x The equation of the line is
m = 2 Answer 2 1
vertical y = – x +
line 7 7
horizontal
line

Write the slope-intercept form for an equation of a
Let’s Begin line perpendicular to the graph of 2y + 5x = 2 that
passes through (0, 6).

Step 1 Find the slope of 2y + 5x = 2.

Perpendicular Line Through a Given Point 2y + 5x = 2 Original equation
2y + 5x – 5x = 2 – 5x Subtract 5x from each side.
Examples 2y = –5x + 2 Simplify.

2y = 5 x + 2
Write the slope-intercept form for an equation of a 2 2 2 Divide each side by 2.
line that passes through (4, –1) and is perpendicular 5
to the graph of 7x – 2y = 3. y = – 2 x + 1 Simplify.

Step 1 Find the slope of the given line.
5
The slope of the given line is – .So
7x – 2y = 3 Original equation 2
the slope of the line perpendicular to this
7x – 2y – 7x = 3 – 7x Subtract 7x from each side. Step 2
line is the opposite reciprocal
–2y = –7 + 3 Simplify. of – , or 2
5
–2y = –7x + 3 Divide each side by –2. 2 5
–2 –2
y = 7 x – 3 Simplify.
2 2

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