Page 439 - Algebra 1

L E S S O N Writing Equations of Parallel and
65
Perpendicular Lines
Warm Up
1. Vocabulary The form for the equation of a line is y - y1 = (52) m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Find the slope and y-intercept.
2. 2x + y = -5 3. -9x + 3y = 12
(49) (49)
4. Write an equation in slope-intercept form for a line that passes through the (52) point (0, -5) and has a slope of _2 .
3
New Concepts Parallel lines are lines that are in the same plane but do not intersect.
Slopes of Parallel Lines
Two nonvertical lines are parallel if they have the same slope and are not the same line.
Any two vertical lines are parallel.
Example The equations y = 2x + 7 and y = 2x - 1 have the same slope, 2, and different y-intercepts. The graphs of the two lines are parallel.
y = 2x + 7
y
4
2
O
y=
2x -
x
1
-2
-4
2
4
Example
1
Determining if Lines are Parallel
Determine if the equations represent parallel lines.
y = - _4 x + 5 a n d 4 x + 3 y = 6 3
SOLUTION
Math Reasoning
Analyze Will one ordered pair ever satisfy the equations of a pair of parallel lines? Explain.
Write both equations in the slope-intercept form y = mx + b.
y = -_4 x + 5 The first equation is already in slope-intercept form.
3
Write the second equation in slope-intercept form by solving for y.
4x + 3y = 6
= -_ 4_x
3y = -4x + 6
3y = - 4x + 6 ___
333
y = - _4 x + 2 3
Since both lines have the same slope but have different y-intercepts, the two lines are parallel.
-_ 4_x
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424 Saxon Algebra 1