9/12/11 3.1 Rectangular Coordinate System
•  Plot points on a rectangular coordinate system.
•  Determine whether ordered pairs are solutions of
equations.
•  Use the distance formula to find distance between two
points.
•  Us the midpoint formula to find the midpoints of line
segments.
Coordinate system – in our city
1 9/12/11 •  What are some of the solutions to this equation in two
variable?
2 9/12/11 Phones
•  The first minute of an international phone call
is $0.96 and $0.75 for each additional
minute. How will you find out a price of any
phone call?
To represent relationships we use
•
min
price
1
0.96
2
1.71
3
2.46
4
3.21
5
3.96
3 9/12/11 Phone call
min
x
price
y
1
0.96
2
1.71
3
2.46
4
3.21
5
3.96
Find the distance between the points.
1.
(4,-2) and (4,6)
2.
(-2,-2) and (4,-2)
3.
(4,6) and (-2,-2)
4 9/12/11 Find the distance between the points.
1.
(x1,y2) and (x1,y1)
2.
(x2,y2) and (x1,y2)
3.
(x1,y1) and (x2,y2)
What is the distance between points (x1, y1)
and (x2, y2) ?
5 9/12/11 Find the midpoint of the line segment that
joins the two points.
1.
(4,-1) and (10,3)
2.
(0,-5) and (2,-8)
3.2 Graphs of Equations
•  Sketch graphs of equations using the point-plotting
method.
•  Find and use x-intercepts and y-intercept as aids to
sketching graphs.
6 9/12/11 Find the x-intercept and y-intercept.
Sketch the graph of each equation.
What does the graph represent?
7 9/12/11 3.3 Slope and Graphs of Linear Equations
•  Determine the slope of a line through two points.
•  Graph linear equations in slope-intercept form.
•  Use slopes to determine whether two lines are parallel,
perpendicular or neither.
•  Use slopes to describe rates of change in real-life
problems.
Find the slope of the line that passes
through the given points.
1.
(2,-5) and (3,-5)
2.
(-3,4) and (-3,8)
3.
8 9/12/11 Sketch the graph of each line.
Which one has larger slope?
1.  A
2.  B
3.  Neither. Their slopes are equal
4.  I am not able to tell
A
B
9 9/12/11 Graph a line whose y-intercept is -2 and
whose slope is 4/5.
A loading dock ramp rises 4 feet above the ground.
1
The ramp has a slope of
.
10
What is the hoizontal length of the ramp?
€
10 9/12/11 Four pumps are emptying four different
pools
Can two lines with positive slopes be
perpendicular to each other?
11 9/12/11 •  Parallel lines – two distinct lines are parallel if and only if they
have the same slope
•  Perpendicular lines – two lines are perpendicular if and only if
the product of their slopes is negative one (are opposite
reciprocals of each other)
Which of the following lines are parallel?
Which of the following lines are perpendicular?
Slope
Rate of Change
m=
change in y Δy y 2 − y1 "rise"
=
=
=
change in x Δx x 2 − x1 "run"
€
12