Download The Slope-Intercept Formula

The Slope-Intercept Formula
Solving an equation for “y”
When you solve an equation for
“y”
You are putting the equation in
“slope-intercept form”
Let’s look at the formula
and it’s parts.
y  mx  b
Represents the numerical
value for the SLOPE of the line
The x and y come from a set of
ordered pairs (x, y). We use this
when writing linear equations.
Represents the y intercept
This is where the
line will cross the yaxis.
Why do we need this
formula?
y  mx  b
We use this formula to WRITE and
GRAPH linear equations.
Solve for Y
Can’t add or sub
these
Why?
They are not
Like Terms
2x  4 y  8
2x
2x
4 y  2 x  8
4
4 4
1
y  x2
2





We want y by itself
Move the x term (do
the opposite + or -)
Move the term in
front of y (do the
opposite x or  )
Slope = ½
Y-intercept = -2
write it as (0, -2)
Write these equations in slope-intercept
form.
To solve for “y” you have to

x  2y  8
x
x
2 y   x  8
2
y
2 2
1
2
x 4
1
Slope = _____________
2

get the “y” by itself.
Use opposite operations to
move everything away from
the “y”




1st – Mark the variable you are
solving for then leave it alone!!
Next – Use opposite operations
to move everything away from
the “y”.
You can’t add –x and 8, so just
bring them down.
Now divide everything by -2.
4
Y - intercept = ________
(0, 4)
Write in slope-intercept form then
name the slope (m) and y-intercept (b).
5x  y  3
4x  2 y  8
4x 3
3
4x
2 y  4x  8
5x  3  y
2
2
y  2x 4
2
1
m=_____
2
4 y  8 x  12
4 4 4
y  2x 3
y  5x  3
5
(0,
4)
1
b=_____
m=_____
2
(0,

3)
1
b=_____ m=_____
(0,3)
b=_____
Write in slope-intercept form then name the
slope (m) and y-intercept (b).
These are special equations. When you only see one
variable, that means the line only touches one axis.
Zero slope and No Slope
Therefore the slope will either be:
1. Zero (0)
y7
y  3
m0
or
These
Equations
Only have
A “y” so
They only
Touch the
“y” axis and
Form
Horizontal
Lines.
Their slope
Is ZERO
2. No Slope
x  2
x5
m
Undefined
These
Equations
Only have
An “x” so
They only
Touch the
“x” axis and
Form
Vertical
Lines.
Their’s Is
UNDEFINED
Now let’s use the formula to
WRITE an equation.
y  mx  b
Write an equation in slope-intercept form when given the
slope and the y-intercept.
m = 3, b = 1
1
y  __
3 x  __
y  3x  1
Simply replace the “m” and the “b”
in the formula with the numbers
and you have an equation.
Write an equation in slope-intercept form when given the
slope and the y-intercept.
Writing Slope-Intercept Equations - Examples
m = -3, b = 5
m=½,b=1
y  3x  5
1
y  x 1
2
m = 0, b = 7
m = 4, b = -2
y  0x  7
y7
y  4x  2