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