Transcript File - Mrs. Malinda Young, M.Ed

Linear Functions &
Graphing from Standard Form &
Graphing Using the Intercepts
Algebra 1
Glencoe McGraw-Hill
JoAnn Evans
A linear equation is the equation of a line. Linear
equations can be written in the form of:
This is known as the Standard Form of a linear equation.
In Standard Form:
1.
A ≥ 0
A must be positive!
2.
A and B can’t both be 0…and they must both be
on the same side!
3.
A, B, and C must be integers with no
3x + 4y = 7
A=3 B=4 C=7
x+
– -2y = 5
A = 1 B = -2 C = 5
8x + 9y = 1
A=8 B=9 C=1
5x +
–- y = 2
A = 5 B = -1 C = 2
A is the coefficient of
the x term and B is the
coefficient of the y term.
C is a constant.
Identify the values of
A, B, and C in the
equations on the left.
Explain why the following equations are
NOT considered to be in standard form.
2x  12  3y
x and y need to be on the left side
of equal sign
y  3x  8
x term comes before the y term
2
xy7
3
“A” is not an integer
 2x  4 y  6
2x  4 y  8
“A” is not greater than or equal to 1
GCF of A, B, and C is not 1
Determine whether the equation is a linear
equation. If it is, write it in Standard Form.
y  5  2x
 2x
 2x
2x  y  5
The power
of the
variables is
one. It is
linear.
Move the x
term to the
left side .
5x  3y  z  2
2xy  5y  6
There are 3
variables.
It is not
linear.
The term
2xy has two
variables.
It is not
linear.
3
x y8
4
3 

4 x   4( y)  4(8)
4 
3x  4 y  32
 4y  4y
3x  4 y  32
The power of the
variables is one. It is
linear. It can be
written in Standard
Form after the
fraction is cleared.
 5x   y  1
y y
 5x  y  1
 1( 5x)   1( y)  1(1)
5x  y  1
The power of the
variables is one. It
is linear. Remember
that A must be
greater than or
equal to 1 to be in
Standard Form.
Efficiency in Graphing………
In the last lesson, graphs were
sketched by creating a table
of values, plotting the
corresponding points, and
drawing the graph through
those points. However, this is
only one of several methods
and is actually the least
efficient of all.
Consider this:
* The graph of any
linear equation is a
line.
* Two points are
all that are needed
to determine a line.
Two convenient points to use would be
the points where the line intersects the
x-axis and the y-axis.
y
Name the
x-intercepts and
the y-intercepts
for the green and
blue lines.
x
The x-intercept is 3. It
occurs at the point (3, 0).
The x-intercept is 1, and
occurs at the point (1, 0).
The y-intercept is - 4. It
occurs at the point (0, - 4).
The y-intercept is 4, and
occurs at the point (0, 4).
The x-intercept of a line occurs when
y = 0 because every point on the
x-axis has a y-coordinate of zero.
Examples:
(- 4, 0)
(-1, 0)
(1, 0)
(3, 0)
y
x
To find the x-intercept
of a line, let y = 0 and
solve the equation for x.
The y-intercept of a line occurs when
x = 0 because every point on the
y-axis has an x-coordinate of zero.
Examples: (0, 4)
(0, 2)
(0, -1)
(0, -5)
y
x
To find the y-intercept
of a line, let x = 0 and
solve for y in the
equation.
Find the x-intercept for the equation x + 5y = 10.
To find the x-intercept, LET y = 0.
x + 5y = 10
x + 5(0) = 10
x = 10
original equation
substitute 0 for y.
solve for x
The x-intercept is 10.
What are the coordinates of the
point on the x-axis where x = 10?
(10, 0)
Find the y-intercept for the equation x + 5y = 10.
To find the y- intercept, LET x = 0.
x + 5y = 10
(0) + 5y = 10
y = 2
original equation
substitute 0 for x.
solve for y
The y-intercept is 2.
What are the coordinates of the
point on the y-axis where y = 2?
(0, 2)
Graph x + 5y = 10 using the intercepts.
The x-intercept is 10.
The y-intercept is 2.
Two points determine a
line. If you know the
x-intercept and the
y-intercept, the line can
be quickly graphed.
Connect the points to
see the graph of
x + 5y = 10.
Use the
intercepts of a
line to sketch a
Quick Graph.
5x + 3y = 15
First, find the x- and y-intercepts.
x-intercept (Let y = 0)
5x + 3y = 15
5x + 3(0) = 15
5x = 15
x=3
y-intercept (Let x =0)
5x + 3y = 15
5(0) + 3y = 15
3y = 15
y=5
The x-intercept is 3.
The y-intercept is 5.
y
x
Find the x- and y-intercept of each equation on
your own:
2x + 3y = 12
x-intercept:
2x + 3(0) = 12
x = 6
y-intercept:
2(0) + 3y = 12
y=4
x-intercept: 6
y-intercept: 4
y
x
-4x + 2y = 10
x-intercept:
-4x + 2(0) = 10
-4x = 10
x = -2.5
y-intercept:
-4(0) + 2y = 10
y=5
x-intercept: -2.5
y-intercept: 5
y
x
x - 4y = 2
x-intercept:
x - 4(0) = 2
x=2
y-intercept:
(0) - 4y = 2
y = -0.5
x-intercept: 2
y-intercept: -0.5
y
x
To find the x-intercept,
let
y equal zero
.
To find the y–intercept,
let
x equal zero
.