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May 24th

May 24th

Reading Graphs and Plotting Points

3.1 Reading Graphs and
Plotting Points

Need to Know
Graph a Scatter Diagram
Graph a Bar Graphs
The Coordinate System
Graphing Ordered Pairs

Rainfall Data for San Diego

California Department of Water Resources
Monthly Precipitation for 2000.

Graph a Scatter Diagram

Month	Rain(in)
Jan	2.05
Mar	1.61
May	.21
July	.02
Sept	.18
Nov	1.13

Graph a Bar Graph

Month	Rain(in)
Jan	2.05
Mar	1.61
May	.21
July	.02
Sept	.18
Nov	1.13

The Coordinate System

Vocabulary
X-axis
Y-axis
Ordered Pair
(x, y)
Origin (0,0)
Quadrants I,
II, III, IV

Graphing Ordered Pairs

Ordered Pairs

(3, 2)
(3, -2)
(-3, 2)
(-3, -2)
(0, 4)
(-2, 0)
(½, -4)

Graphing Table Data

Table Data

x	y
5	-3
-2	-2
-1	4
3/2	5

Analysis Example

U.S. college enrollment
has grown from 60.3
mill. in 1990 to about
68.3 mill. in 2000.

a) Approximate the
enrollment for 96.

b) Predict the
enrollment for 2005.

3.2 Graphing Linear Equations

Need to Know
Idea of solutions to linear
equation in 2 variables
Checking a solution to a linear
equation in 2 variables
How to find solutions to linear
equation in 2 variables

The Main Idea -
Solutions to 2 Variables Equations

One Variable Equation

x + 2 = 8

Two Variable Equation

x + 2y = 8

One Variable Equation

x + 2 = 8

Variables
Solution
Graph

Two Variable Equation

x + 2y = 8

Variables
Solution
Graph

Linear Equations in 2 Variables

Definition of a linear equation, is
any equations that can be written in
the form of

where m, b, A, B and C are constants.

It’s graph is always a line.

Checking a Solutions

Are the points solutions to the equation 2x – 3y = 12?

How to Find Solutions

Find a solutions to 2x + y = 8
Think about the mental steps
1.
2.
3.

Graphing Linear Equations

Graph the equation

Solve for y then

end

3.3 More Graphing: Intercepts

Need To Know
What are the intercepts
How to find intercepts
How to graph with intercepts
Graphing Special Equations

Intercepts – What are they?

Intercepts
The x-intercept of a line is the
x-coordinate of the point
where the point crosses the
x-axis.

The y-intercept of a line is the
y-coordinate of the point
where the point crosses the
y-axis.

Intercepts – How to find them?

The x-intercept

The y-intercept

Find the intercepts for :
3x – 4y = -12

Practice Graphing w/ Intercepts

Find the intercepts and graph
–2x – y = -6

Find the intercepts and graph

Finding Intercepts

This is a graph of a
non-linear equation.
Find the intercept
points.

Graphing Special Equations

Graph the equation y = -2

x	y

Graph the equation x = 4

x	y

Conclusion

Always Remember:
x = number is a vertical line
y = number is a horizontal line

3.4 Rates

Need To Know
Understanding Rate of Change
Visualizing Rate of Change

Rate of Change

Definition:
A rate is a ratio that indicates how two
quantities change with respect to each other.

Examples:
1. The virus is growing 2000 cells every minute.
2. My car is getting 25 miles per gallon.
3. Tristan Gale went 2.2 miles in 1 min 45.11 sec to win the
gold medal in skeleton.

Calculating Rates

The company car you took on a business trip
read 25,398 miles at the start and 25,719 miles
at the end of the trip. You paid $16.50 for 13
gallons to fill the car back up. What is the rate
of gas con sumption in miles per gallon?

Visualizing Rates

spending for NASA is represented in the chart . At what rate is the amount spent on NASA changing?
The fol lowing graph shows data from a recent AT&T phone call between Burlington, VT and Austin TX. At what rate was the customer being billed?	cents
		Length in minutes

end

3.5 The Slope of a Line

Need to Know
The idea of slope
Slope characteristics
3 ways to find slope

The Idea of Slope

Slope is the measure of the steepness of a line.

We can measure slope by comparing
vertical change to horizontal change .

The Measure of Slope

The ratio of change comes from two distances,
so we find each distance by subtraction .

Practice – 3 Ways to Find Slope

Find Slope
1. From a picture

2. From the formula

3. From an equation

Find Slope of the line.

Find Slope
1. From a picture

2. From the formula

3. From an equation

Find Slope of the line
through (-5,1) and (4,-6)

Find Slope
1. From a picture

2. From the formula

3. From an equation

Find Slope of the line
through (-2,-3) and (4,-4)
You try it!

3.6 The Equation of a Line

Need To Know
Graphing with a slope and intercept point
Idea of the slope-intercept form of the
equation of a line
How to write equations of lines

Graphing Slope and Intercepts

Graph the line with the slope of –2/5 and a y-intercept of 4.
Graph the line with the slope of 3 and a y-intercept of -2.

A Model for Learning Math

Equations of lines

WINDOW

Xmin = -6 Xmax = 6

Ymin = -6 Ymax = 6

Graph and observe patterns
Graph and observe patterns

Slope-Intercept Form
for the Equation of a Line

y = mx + b
m = the slope of the line
b = the y coordinate of the y-intercept
or (0, b) is the y-intercept point

Graphing y = mx + b

Find the slope and the
y-intercept and graph

Writing an Equation for a Line

To write and equation of a line you …

Write the equation of the line with a slope of
–3 and a y-intercept through the point (0, 5).

Write the equation of the line with a slope of
2/3 and a y-intercept through the point (0,-11).

Need:
1. A point
2. A formula
3. A slope

end

3.7 Point-Slope Form

Need To Know
Idea of the point-slope form of the
equation of a line
How to write equations of lines
Graphing with a point and a slope

Writing an Equation for a Line

y = mx + b is not always the best way
to write an equation for a line.

The next problem illustrates a dilemma
which will leads us to a need for a new
and better equation.

Write the equation of the line through the point
(-4, 1) and the point (2, 3).

Need:
1. A formula:
y=mx+b
2. A point
3. A slope