Download 4-5B Writing Equations in Standard Form

4-5B Write an Equation in
Standard Form and in SlopeIntercept Form
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
Remember:
slope-intercept form
y  mx  b
and
point-slope form
y  y1  mx  x1 
In this lesson you will write the equation of a line given in
point-slope form into standard form.
Do you remember the standard form for a linear equation?
Ax + By = C
In standard form,
the variable terms
are onThe
theAleft
side
is the
of
the equalof
sign
coefficient
the x
term while the B is
the coefficient of
the y term! C
represents a
constant.
and the
constant term
is on the right
side.
In standard form A > 0, and A and B are not both zero and
A, B, and C are integers with a greatest common factor of
1.
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.
 2x  4 y  6 “A” needs to be greater than or equal to one.
2
xy 7
3
2x  4 y  8
“A” is not an integer.
GCF of A, B, and C is not 1.
5
Write y  5   x  2 in standard form with integer
coefficients. 4
What do the
instructions “integer
coefficients” mean?
REAL NUMBERS
Integers: Whole numbers and their opposites
(this means positive and negative whole numbers).
ex: … ‫ ־‬4 ,‫ ־‬3 ,‫ ־‬2 ,‫ ־‬1 ,0 ,1 ,2 ,3 ,4 …
Whole Numbers: Natural Numbers and
zero. ex: 0,1,2,3…
Natural or Counting Numbers
ex: 1,2,3,4,…
5
Write y  5   x  2 in standard form with integer
coefficients. 4
What do the
instructions “integer
coefficients” mean?
Positive or negative
whole numbers in front
of the variables.
NO FRACTIONS
or DECIMALS
as
COEFFICIENTS!
5
Write y  5   x  2 in standard form with integer
coefficients. 4
How can you get an integer coefficient for x?
5
5
Could you use the reciprocal of ? y  5   x  2
4
44
Multiply each side of the
 4  y  4  5 5
 3 x  5

y  5     x  2 
equation by 4 to clear the

5
 5  4 4
 4
denominator.
4 y  20   5 x  2
No, using the
reciprocal just
Distribute.
4 y  20  5x  10
gives the
 20
 20
Subtract 20 and simplify.
fraction to the
4 y  5x  10
Addother
5x tovariable!
both sides.
 5x
 5x
5x  4 y  10
Copy in
your
spiral
notebook!
3
Write y  3  x  4  in standard form with integer
coefficients. 5
3
Multiply each side of the
y  3  x  4 
5
equation by 5 to clear the
denominator.
y  3   3 x  4 
5
Distribute.
5y  15  3 x  4 
Add 15 and simplify.
5y  15  3x  12
 15
 15
Subtract 3x to both sides.
5y  3x  3
Undo the negative value for “A”.  3x
 3x
 3x  5y  3
1 1 1
3x  5y  3
Write in standard form with integer coefficients.
Example 1
1
y  3   x  7 
8
Example 3
y  5  3x  3
Example 2
y  4  2x  3
Example 4
3
y  1  x  5 
4
Write in standard form with integer coefficients.
Example 1
1
y  3   x  7 
8
1

 8 y  3   8  x  7 
 8
 8y  24  x  7
 24  24
 8y  x  17
x
x
 x  8y  17
1 1 1
x  8y  17
Example 2
y  4  2x  3
y  4  2x  6
4
4
y   2x  2
 2x
 2x
2x  y  2
Write in standard form with integer coefficients.
Example 3
y  5  3x  3
y  5  3x  9
5
5
y   3x  4
 3x
 3x
3x  y  4
Example 4
3
y  1  x  5 
4
3

4y  1  4 x  5
 4
4 y  4  3x  5
4 y  4  3x  15
4
4
4 y  3x  19
 3x  3x
 3x  4 y  19
1 1 1
3x  4 y  19
Next in this lesson you will write the equation of a line
given in point-slope form into slope-intercept form.
slope-intercept form
y  mx  b
1
Write y  2  x  5 in slope-intercept form.
2
1
y  2  x  5
Write the equation.
2
1
5
y

2

x

Distribute the slope.
2
2
4

Add 2 to each side
2
2
and simplify.
1
9
y  x
2
2
Copy in
your
spiral
notebook!
1
Write y  2  x  5 in slope-intercept form.
2
1
y  2  x  5
Write the equation.
2
1

Undo the fraction.


2
2y  2   x  5
2
2y  4  x  5
Simplify.
4
4
2y  x  9
2 2 2
Another method:
1
9
y  x
Copyundo
in
You could
2
2
your
the fraction!
spiral
notebook!
Write in slope-intercept form.
Example 5
Example 6
y  9  6x  7 
y  6  2x  5
y  9  6x  42
9
9
y  6x  33
y  6  2x  10
6
6
y  2x  4
Example 7
3
y  4  x  6
4
3
18
y4  x
4
4
3
9
y4  x
4
2
8

2
4
4
3
1
y  x
4
2
Write in slope-intercept form.
Example 8
3
 1x  3
2
3
6
y   x 3
2
2
3
3


2
2
3
y x
2
y
Example 9
Example 10
2
1

3
y   2 x  
y  5  x  7 
3
4

4
3

2
1
4 y  5  4  x  7 
y   2x 
4
3
2
4 y  20  3x  7 
 y  2     2x  1  6
6
 

4 y  20  3x  21
3 
2

 20
 20
6y  4  12x  3
4
4
4 y  3x  1
6y  12x  7
4 4 4
3
1
6
6
6
y  x
7
4
4
y  2x 
6
Summary
Equations of Lines
Slope - Intercept Form : y  mx  b
Point - Slope Form : y  y1  mx  x1 
Standard Form : Ax  By  C
Horizontal Line (zero slope) : y  c
Vertical Line (undefined slope) : x  c
4-A12 Pages 223−224 # 26–41,48–54.