Unit 3.6 !
Date:!__________
Slope-intercept form.
A line may be graphed MANY ways.
One way to graph is to randomly
select x values and calculate the
corresponding y values.
y = 4x + 2
x y
(
(
(
,
,
,
)
)
)
Another way, was to select two
specific points, the intercepts.
x-int., let y = 0
(
,
)
y-int., let x = 0
(
,
)
1
y =− x−3
3
This section points out some facts about linear equations
in two variables that will provide still a 3rd (and
best) method for graphing. But first consider:
Graph the line whose
y-intercept is (0, 2 )
And that has a slope of
m=
1
4
EQUATIONS IN SLOPE-INTERCEPT FORM
y = 2x + 3
Consider an equation:
!
!
!What would the y-intercept be?
To determine the slope of the line, find two ordered pairs
and compute the slope formula.
! x y
0 3
y 2 − y1
m=
x 2 − x1
It is not just a coincidence unique to the previous
equation. Given any equation in the form:
y = mx + b ,
!
!
it is said to be in slope-intercept form and it
represents a line of slope m with y-intercept (0, b ).
Ex. 2)! Find the slope and y-int. for the following eq.
4
y = x−8
y − int. =
5
! a)!
!
!
!
!
!
b)! 2x + y = 5 !
y − int. =
!
!
m=
!
c)! 3x − 4 y = 7 !
y − int. =
!
!
m=
!
!
!
!
!
m=
12
Ex. 3)! A line has a slope of 5 and a y-intercept of
(0,11). Find the equation of that line. Your
equation should be of the form: y = mx + b
−
Ex. 4)! ROO
Graphing and Slope-intercept Form. Recall from Ex. 1, we
were able to draw a line w/out an eq. Now that
we have an equation, we can pull out the pieces of
information that made that possible.
Ex. 5)
a)
Graph:
y=
3
x+5
4
y − int. =
m=
Ex. 5b) Graph: 2x + 3y = 3
Note this is not in slopeintercept form. You can’t draw any
data from it until it is.
y − int. =
m=
PARALLEL AND PERPENDICULAR LINES
Parallel means that two lines running side by side, never
cross. When looked at on a grid, they would have
the same slope.
Ex. 6)
Are the lines parallel?
y = −3x + 4
6x + 2y = −10
y − int. =
m=
y − int. =
m=
The relationship between the slope of lines that are
perpendicular is not as straight forward.
Perpendicular lines form a 90 degree angle where
they cross.
Are the lines perpendicular?
y = 3x − 5
1
y =− x+4
3
y − int. =
m=
y − int. =
m=
Look at the two lines graphed above. What is the product
of their slopes? This is also not just a coincidence.
The product of the slopes of perpendicular lines
will always be (-1).
! ! !
The slope of the first line times
! ! !
the slope of the second line equals -1.
( m )( m ) = −1
1
2
Ex. 7)! Determine whether the graphs of 2x + y = 8 and
1
y = x+7
2
are perpendicular.
Ex. 8)! Write a slope-intercept
equation for the line whose
graph is described.
! a)! Parallel to the graph of
2x − 3y = 7 , with a yintercept of (0,-1)
!
!
b)! Perpendicular to the graph of 2x − 3y = 7, with a
y-intercept of (0,-1)