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Math 1513 Sec 1.4
1
Section
1.4
Equations of Lines and Modeling
Consider the three linear equations below:
a.
4
3
y
x
b.
4
3
5
y
x
c.
4
3
3
y
x
What are the slopes and
y
-intercepts of these lines?
These equations are written in
Slope-Intercept
form:
y mx b
where
m
is the slope and
b
is the
y
-intercept.
Enter these 3 equations into your calculator as Y1, Y2, and Y3
and draw the graph.
Sketch the graph
from your screen:
These graphs illustrate a very important fact:
Non-vertical lines are
parallel
if and only if they have the same
slope and different
y
-intercepts.

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*Sign up* Math 1513 Sec 1.4
2
Now enter this equation for Y4:
3
4
2
y
x
This last equation has a special relationship to the other 3 lines.
The first 3 lines have a slope of
4 3
and the last equation has a
slope of
3 4
and
(4 3)( 3/4)
1
.
This example is suppose to illustrate another fact:
Two lines with slopes
1
m
and
2
m
are
perpendicular
if and only
if the product of their slopes is -1.
That is,
1
2
1
m m
.
The fourth line we graphed is supposed to be perpendicular to
the other three lines.
However, it doesn’t look like it.
What’s wrong?
What could we do on the calculator to make
the lines look perpendicular?

Math 1513 Sec 1.4
3
Finding equations of lines using the Point-Slope form.
a.

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