Download Algebra 1 Chapter 3 Power Point

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts
no text concepts found
Transcript
What do you know about
Linear Relations?
What does Linear look like?
0 On a graph-
0 In a table –
0 As an equation-
0 Straight line
0 Constant rate of change
0 Unit rate is always the
same
0 Ratio of Change in y
divided by the change in
x
The x and y variables
have an exponent of 1
Which are Linear Equations
Y = 4 – 3x
2x – 3y = 5
2/3x – 1/4y = 12
X2 – 3 = y
8 = x/y
1/3 y = -1
6x – xy = 8
Standard Form
The standard Form of a Linear
Equation is
Ax + By = C, where A > 0,
and A, B, and C are all integers with a
GCF of 1.
Put Each in Standard Form
Linear Equations
Standard Form
y = 4 – 3x
2/3x – 1/4y = 5
1/3 y = -1
-5x + 2y = -9
4/5y – 2/3x = 3/2
3x + y = 4
8x – 3y = 60
y = -3
5x – 2y = 9
20x – 24y = 45
Intercepts
0X- Intercept
0Where the line
0Y- Intercept
0Where the line
passes through
passes through
the x axis
the x axis
0Set y=0
0Set x = 0
0In a table, where 0In a table, where
y=0
x=0
Graphing Equations in
Standard Form
0 Using an Equation
2x + 4y = 16
in Standard Form
y = 4 – 3x
0 Two Points
1/3y
=
-1
determine a line
0 Find the X and Y x = 2/5y + 4
intercepts
Graphing Relations in a Table
0Using a Table of
Values
0 Find three to
four points in a
T-chart and plot
the points
Y = 1/3x + 5
2x – y = 2
X=3
Which equations are Linear??
2x – 8 = y
6 = 2/5 x – y
2x2 – y = 8
xy = 6
7 + 3x -6 = 3x + 1
2x – 4 = 2x - 6
Linear Equations have one or
no solutions
0The solution or root of a function is
any value that makes the equation
true
0The value that makes the equation
true is the x-intercept
Function Notation and Roots
of an Equation
0 A linear function is a function for which
the graph is a line
0 The simplest linear function is f(x) = x
0 You can find the root of an equation by
graphing it’s related function. To write
the related function replace y with f(x)
and set f(x)=0.
Find the Zeros, Roots,
Solutions
2x – 8 = y
0 Steps
f(x) = 0
6 = 2/5 x – y
3x + 7 = 3x + 1
2x – 8 = 2(x – 4)
0 = 2x – 8
0 = 2/5 x – 6
No solution, no x-intercept
horizontal line
Infinite solutions
0 Non-linear
Related documents