Page 441 - Algebra 1

Caution
Pay attention to whether a problem is asking
to write the equation
for a parallel line or a perpendicular line.
Example
4
Writing Equations of Perpendicular Lines
Write an equation in slope-intercept form for the line that passes through (-2, -3) and is perpendicular to a line with equation y = -3x + 1.
SOLUTION
The slope of y = -3x + 1 is -3. Any line perpendicular to the given line has a slope of _1 , which is a negative reciprocal of -3.
Substitute m = _1 and the point (-2, -3) into the point slope formula. 3
Write the equation in slope-intercept form. y-y1 =m(x-x1)
y - (-3) = _1 (x - (-2)) 3
y + 3 = _1 x + _2 33
y = _1 x - 2_1 33
Substitute the slope and point into the equation. Simplify.
Subtract 3 from both sides and simplify.
3
Example
5
Application: Coordinate Geometry
Use the slopes of the line segments to show that LMN is a right triangle.
SOLUTION
−−−
to MN. Find the slope of LM −−−
LMN is a right triangle if LM is perpendicular −−− −−−
and MN.
−−− y2 - y1 1 - (-3) 4 ___
426 Saxon Algebra 1
b.
(Ex 2)
c.
(Ex 3)
332
Write an equation in slope-intercept form for the line that passes
through (-3, 2) and is parallel to a line with equation y = _4 x + _5 . 77
Determine if the lines passing through the points are perpendicular. line 1: (-2, 2) and (2, -4) line 2: (3, 6) and (5, 3).
slope of LM = x2 - x1 = -3 - (-2) = ____
a.
Determine if the equations represent parallel lines.
-1 = -4 −−− y2 -y1 -3-(-2) -1 1
slope of MN = x2 - x1 = -2 - 2 = -4 = 4 −−− −−−
The slopes of LM and MN are negative reciprocals, so the two sides are perpendicular. Therefore, LMN is a right triangle because it contains a right angle.
Lesson Practice
(Ex 1)
y=_2x+5_1 and_3x+y=1
4
y
2
L
O
x
-4
2
4
-2
N
M
-4