Page 440 - Algebra 1

Example
2
Writing Equations of Parallel Lines
Write an equation in slope-intercept form for the line that passes through (-1, 1) and is parallel to a line with equation y = 2x - 1.
SOLUTION
Determine the slope of the parallel line. Then substitute the slope and the point into the point-slope formula.
The slope of the line y = 2x - 1 is 2. Any line parallel to the given line has a slope of 2.
Substitute m = 2 and the point (-1, 1) into the point-slope formula. Write the equation in slope-intercept form.
y-y1 =m(x-x1) y - 1 = 2(x + 1) y - 1 = 2x + 2
Substitute the slope and point into the equation. Distributive Property
Add 1 to both sides.
y = 2x + 3
Theequationof thelineisy=2x+3.
Perpendicular lines are two lines that intersect at right angles.
Slopes of Perpendicular Lines
Any two lines are perpendicular if their slopes are negative reciprocals of each other. A vertical and horizontal line are also perpendicular.
Example The slope of y = 3x - 7 is 3.
The slope of y = -_1 x + 3 is -_1 . Since the
33
slopes are negative reciprocals, the lines are
perpendicular.
y = - _1 x + 3 3
-4
-2
-2
-4
y
4
2
O
4
x
y = 3x - 7
Math Language
The reciprocal of a number n is _1 . The
product of a number and its reciprocal is 1.
n
Example
3
Determining if Lines are Perpendicular
Determine if the lines passing through the given points are perpendicular. line 1: (-5, 4) and (-3, 0) line 2: (-2, -2) and (-4, -3) SOLUTION
Find the slope of each line.
m = y2 - y1 m = y2 - y1 __
__
-3 -(-5) -4 -(-2)
1 x2 - x1 2 x2 - x1
= 0 - 4 = -3 -(-2)
= _- 4 = _- 1 2 -2
= - 2 = _1 2
Since -2 is the negative reciprocal of _1 , the lines are perpendicular. 2
Lesson 65 425