MATH 80 UNIT 3.4
I.
SUPPLEMENT
FINDING EQUATIONS OF LINES
There are two very useful formulas to find the equation of a line. They are:
a.
The slope-intercept formula:
This formula can be used to find an equation of the line if the slope m, and a point (x,y) is
given.
b.
The slope formula:
With this formula and the slope-intercept formula we can find the equation of a line,
given two points (
Example 1
) and (
)
Find the equation of the line with slope , passing through the point (
SOLUTION:
).
Since we know the slope of the line, we can use the slope-intercept formula
(
). Remember that m is the slope, so we plug in for m.
So:
Now we use the point (
) for (
).
Plug in 2 for x and 4 for y.
( )
Thus, the equation of the line is:
(Notice that the equation of a line has x and y in it)
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.
PAGE 2
Exercise 1
Find the equation of each line, given the slope and one point on that line.
1.
(
)
(
)
3.
(
)
(
5.
(
)
(
EXAMPLE 2
Find the slope of the line passing through the points (-2, 6) and (3, -5)
)
)
2.
(
)
(
)
4.
(
)
(
)
6.
(
)
(
)
SOLUTION: Here we use the slope formula:
Because we were given two points, and we weren’t given the slope
).
We can use either point for(
Se we let (
)
(
Thus:
(
) and (
)
(
)
) ( )
( ) (
)
Therefore, the slope of the line passing through the points (
(
NOTE:
) is
) and
.
Since we can use either point for (
) , let’s see what will happen if we let
(
)
)
Then
(
) and (
(
(
) (
)
(
)
)
Notice that we got the same answer as above.
[MATH 80 SUPPLEMENT: 3.4]
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.
PAGE 3
Find the equation of the line passing through the points (
EXAMPLE 3
) and (
)
SOLUTION: First we realize that the slope of the line is not given. So, as in example 2, we
must use the equation:
We let (
)
(
to find the slope.
) and (
)
(
Then:
).
This is the slope
Now that we know the slope, we can solve the problem by using the slope-intercept formula.
( )
( )
( )
( )( )
( )
( )( )
So, in both cases we found m (slope) and b (y-intercept) of the equation:
Therefore, the equation is:
EXERCISE 2
Find the equation of the line passing through the points:
1. (
3. (
5. (
) (
) (
)
2. (
)
) (
4. (
)
6. (
) (
)
) (
)
) (
)
[MATH 80 SUPPLEMENT: 3.4]
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.
.
PAGE 4
ANSWERS-EXERCISE 1
(
1.
)
(
)
(
2.
( )
( )
)
(
)
( )
( )(
)
(
So:
)
( )( )
So:
(
3.
(
(
)
)
(
)
(
)
(
)
)(
)
( )
(
)
(
)
So:
(
)
(
)
( )
( )
)
( )
So:
5.
(
4.
6.
(
)
( )
( )( )
So:
( )
( )( )
So:
[MATH 80 SUPPLEMENT: 3.4]
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.
PAGE 5
ANSWERS-EXERCISE 2
1.
(
)
(
(
)
(
)
2.
)
(
)
( )
(
)
( )
( )=( ) ( )
(
So:
So:
3.
4.
)
( )( )
or
(
(
) ( )
( )
( ) ( )( )
)
(
) (
( )
( ) ( )(
So:
)
)
So:
or:
5.
(
(
)
(
)
(
)
) (
( )
( )( )
6.
)
So:
(
(
(
)
) (
( )
( )( )
)
)
So:
[MATH 80 SUPPLEMENT: 3.4]
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.