Download Sec 3.7 Equations of Lines in the Coordinate Plane

Sec 3.7 Equations
of Lines in the
Coordinate Plane
Chapter 3
Review

If two lines are cut by a
transversal they form
special properties.



Corresponding angles
Alternate interior angles
Alternate exterior
angles
Are congruent.
Are parallel


Same-side interior
angles are
supplementary.
 Two
lines  to the same
line are to each other.
 In
a plane, two lines 
to the same line are .
Lesson Purpose
 Objective
 Essential
 Write
 How
an equation of a
line given
characteristics of
parallel or
perpendicular lines.
Question
can you prove
that two lines are
parallel?
What is a slope?
 The
steepness of
a hill
Different types of slopes
A positive(+) slope:
A negative(-) slope:
If you go from left to right
 and you go up, it is a
positive slope
If you go from left to right
 and you go down, it is a
negative slope
A zero (0) slope:
If you go from left to right
and you don't go up or
down, it is a zero slope
No Slope or
Slope Undefined
Vertical lines have no
slope, or undefined slope.
Ski Bird cannot ski vertically. Sheer
doom awaits Ski Bird at the bottom of a
vertical hill.
Slope Equation
A


slope of a line contains two points
(x₁, y₁) and (x₂ ,y₂).
Example #1
 Let’s
find the slope of
the line passing
through the given
points.
 (2,3),(-1,-6)
 Step
1: use slope
equation:
 Step
2: set up equation
with points given:
 Step
3: solve
 What
kind of slope is it?
Question #1
 What
is the slope of the line passing
through the points (2, 7) and (21, 3)?
 A.
2/7
 B. 3/4
 C. 4/3
 D. 1/3
Question #2
 What
is the slope of the line passing
through the points (-2,-3) and (1, 3)?
 A.
1/2
 B. 2
 C. -2
 D. -1/2
Example #2
 What
is the slope of
the line?
Question #3
 Find
the slope of the
line?
 A.
1/4
 B. -1/4
 C. -4
 D.
4
Question #4
 Find
the slope of
the line?
 A.
2/3
 B. 3/2
 C. -2/3
 D. -3/2
3.8 Slopes of Parallel lines
 Parallel
lines have the same slope.
Slopes of Perpendicular Lines
 The
product of the slopes of two
perpendicular lines is -1 or the slopes are
negative reciprocal.

Product means multiplication.
Slope-Intercept Form
 -is
an equation of a
non-vertical line is
 y=mx+b
 where m is the slope
and b is y-intercept
Example #3
 Graph
the equation of the line y=
½x+2
 Step
1: identify the slope and yintercept
 Step
2 : plot your y- intercept
 Step
3: connect the points
Question #5
 Graph
A.
C.
the equation y= ½x-3
B
D.
Question #6
 Graph
A
C
the equation y= -2x-2
B
D
Real World Connections
Ticket Out and Homework
 Is
it always necessary to
identify both the slope
and y-intercept of a
line when graphing its
equation? Explain
 pg.
207-208 #’s 5, 6,
7,9,10, 14, 15,
18,19,20,21