3.6/3.7: Lines in a Coordinate Plane
Your mother was a hamster and your father smelt of elderberries.
Your mother was a hamster and your father smelt of elderberries.
-French Soldier
Algebra 1 Review
Slope of a Line: Ratio of its vertical change to the corresponding
horizontal change (“rise over run”)
y
Rise y 2  y1
Slope =

Run x 2  x1
x2  x1
P2 (x2, y2 )
y2  y1

P1(x1, y1)



x

Algebra 1 Review
Slope of a Line: Ratio of its vertical change to the corresponding
horizontal change (“rise over run”)
y
Rise y 2  y1
Slope =

Run x 2  x1
P2 (11,6)
P1(2,3)


x

Algebra 1 Review
Find the slope of the line below.
Algebra 1 Review
Graph the line that contains the point (2,1) and the slope of…
1
1) m 
4



2) m  2
3) m  0
Forms of a Line
Slope-Intercept Form: y  mx  b
m = slope b = y-intercept
 Ax  By  C
Standard Form:
A,B are integers ≠ 0 and A > 0

1
Ex : y  x  3
2


Point-Slope Form: y  y1  m(x  x1)
m = slope (x1,y1) = point on line
Ex : x  2y  6
1
Ex : y  3  (x  0)
2
Graphing Lines in Slope-Intercept Form
3
Graph the line y  x  2 .
4

Graphing Lines in Standard Form
Graph the line 2x + 3y = 6.
Find intercepts
Using Point-Slope Form
Write an equation in point-slope form of the line through point
P(-1,4) with slope 3.
Write an equation in point-slope form of the line through the
points A(-2,3) and B(1,-1).
Horizontal and Vertical Lines
Let’s take a look at the vertical line and horizontal line through
the point (-3,1).
Horizontal Lines
Slope = 0
Equation: y  b
Vertical Lines

Slope Undefined
Equation: x  a
Horizontal and Vertical Lines
Write equations for the horizontal line and the vertical line that
contain the point (2,-5).
Slope and Parallel Lines
Slopes of Parallel Lines:
1) If two nonvertical lines are
parallel, their slopes are equal.
2) Any two vertical lines are
parallel.
Slope and Parallel Lines
Are lines l and m parallel?
(1,5)
(3,3)
(-2,-4)
l
(1,-4)
m
Slope and Perpendicular Lines
Slopes of Perpendicular Lines:
1) If two nonvertical lines are
perpendicular, their slopes are
opposite reciprocals.
2) Any horizontal line and vertical
line are perpendicular.
Slope and Perpendicular Lines
Are lines l and m perpendicular?
(-2,3)
(0,2)
m
l
(-3,-2)
(6,-3)
Parallel and Perpendicular Lines
Write an equation in point-slope form for the line parallel to
3x + y = 4 containing the point (-1,2).
Write an equation in point-slope form for the line perpendicular
to y = -3x - 5 containing the point (-3,7).
Parallel, Perpendicular, or Neither
Are the following pairs of lines parallel, perpendicular, or neither?
JUSTIFY your reasoning.
1
y   x 1
1)
3
4 y  12x  20


2)
3y  12x  18
1
y  x3
4


y  3x 1
3)
3y 12x  21
3.6/3.7: Lines in a Coordinate Plane
HOMEWORK:
p.169 #3-7 odd,
19-25 odd, 29
p.177 #4-12 even,
18-22 even
THT:
DUE
TOMORROW!!!
Evil will always triumph over good because good is dumb.
Evil will always triumph -Dark
over good
because good is dumb.
Helmet