2.5 writing equation of a line part 2 september 21, 2012
TRANSCRIPT
2.5Writing Equation of a Line
Part 2September 21, 2012
In a coordinate plane, 2 lines are parallel if and only if
they have the same slope.
Slopes of Parallel Lines
Write Equations of Parallel Lines
–The given line has a slope of 2. Any line parallel to this line will also have a slope of 2. –
Write an equation of the line that passes through and is parallel to the line .5= 2xy +–
( )41,–
y = mx + b4 =-2(-1) + b4 = 2+ b-2 -22 = by = -2x + 2
Simplify
Solve for b
Substitute 4 for y, -1 for x and -2 for m
Another Example
Find the equation of a line going through the point (3, -5) and parallel to
Using the point-slope equation where the slope m = -2/3 and
the point is (3, -5) we get
83
2 xy
)3(3
2)5( xy
23
25 xy
33
2 xy
b)( 33
25
b 25
b 3
33
2 xy
OR
Find the equation of the line going through the point (4,1) and parallel to (click mouse for answer) 3 7y x
1 3 4
1 3 12
3 13
y x
y x
y x
Find the equation of the line going through the point (-2,7) and parallel to (click mouse for answer) 2 8x y
7 2 2
7 2 2
7 2 4
2 3
y x
y x
y x
y x
Checkpoint
133
13
121
)4(31
xy
b
b
b
32
3
47
)2(27
xy
b
b
b
In a coordinate plane, 2 lines are perpendicular if and only if their slopes are opposite reciprocal of
each other (or their product is –1)
Slopes of Perpendicular Lines
Find the equation of a line going through the point (3, -5) and perpendicular to
The slope of the perpendicular line will be m = 3/2. Using the point-slope
equation where the slope m = 3/2 and the point (3, -5) we get
Equation of a line Perpendicular to another line
83
2 xy
)3(2
3)5( xy
2
9
2
35 xy
2
19
2
3 xy
2
19
2
32
192
95
)3(2
35
xy
b
b
b
Find the equation of the line going through the point (-6, -5) and perpendicular to y = -x + 2.
Find the equation of the line going through the point (-2,7) and perpendicular to 2 8x y
17 2217 2217 121 82
y x
y x
y x
y x
Checkpoint
1= xy +
Homework:
2.5 p.98 #37-42ALL, 44-50even