Download Graphing Linear Equations Chapter 7

Chapter 7
Graphing
Linear
Equations
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-1
Chapter Sections
7.1 – The Cartesian Coordinate System and
Linear Equations in Two Variables
7.2 – Graphing Linear Equations
7.3 – Slope of a Line
7.4 – Slope-Intercept and Point-Slope Forms of
a Linear Equation
7.5 – Graphing Linear Inequalities
7.6 – Functions
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-2
2
The Cartesian
Coordinate System and
Linear Equations in
Two Variables
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-3
3
Definitions
A graph shows the relationship between two
variables in an equation.
The Cartesian (rectangular) coordinate system is
a grid system used to draw graphs. It is named
after its developer, René Descartes (1596-1650).
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-4
4
Definitions
y
II
I
III
IV
x
The two intersecting axis form four quadrants,
numbered I through IV.
The horizontal axis is called the x-axis.
The vertical axis is called the y-axis.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-5
5
Definitions
y
Origin
x
(0, 0)
The point of intersection of the two axes is called
the origin.
The coordinates, or the value of the x and the
value of the y determines the point. This is also
called an ordered pair.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-6
6
Plotting Points
Starting at the
origin, move 3
places to the right.
Plot the point (3, 5).
The x-coordinate is 3 and the y-coordinate is 5.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-7
7
Plotting Points
Then move
5 places up.
Plot the point (3, 5).
The x-coordinate is 3 and the y-coordinate is 5.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-8
8
Plotting Points
(3, 5)
Plot the point (3, 5).
The x-coordinate is 3 and the y-coordinate is 5.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-9
9
Linear Equations
A linear equation in two variables is an
equation that can be put in the form
ax + by = c
where a, b, and c are real numbers.
This is called the standard form of an equation.
Examples:
4x – 3y = 12
y = 5x + 3
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-10
10
Solutions to Equations
The solution to an equation is the ordered pair
that can be substituted into the equation without
changing the “validity” of the equation.
Is (3, 0) a solution to the equation 4x – 3y = 12?
4x – 3y = 12
4(3) – 3(0) = 12
12 – 0 = 12
12 = 12  Yes, it is a solution.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-11
11
Graphing
A graph of an equation is an illustration of the
set of points whose coordinates satisfy the
equation.
A set of points that are on a line are collinear.
The points (–1, 4), (1, 1)
and (4, –3) are collinear.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 7-12
12