#
Section 2-7

#
Finding the Equation of a Line

##
Finding the Equation of a Line Given Two Points

If you are given the coordinates of two points on the line, you can find the
equation in
point-slope form
fairly easily. First use the horizontal and vertical
change between the two points to find the
slope
, and then use either one of
the
ordered pairs
to write the equation in point-slope form.

Example:

Find the equation of a line through the points

(4, 3) and (7,
**
–
**
2).

First, find the slope.

Now, use either point to write the equation in point-slope form.

##
Finding the Equation of a Line Parallel to a Given Line

Sometimes you may be given a linear equation and asked to find the equation
of a second line which shares some characteristics.

Example:

Find an equation in slope-intercept form of the line that has the same slope
as

5
*
x
*
= 10
*
y
*
**
–
**
2

and contains the point (5,
**
–
**
3).

First step: Find the slope of the given line. To do this,
put the equation in
slope-intercept form
. Divide both sides by 10:

Now get
*
y
*
alone on one side.

So the slope is 1/2.

Now, using point-slope form with
*
m
*
= 1/2,
*
x
*
_{
1
}
=
5, and
*
y
*
_{
1
}
=
**
–
**
3, we get the slope of the desired line:

The final step is to change this into slope-intercept form.
This just means getting rid of the parentheses and making sure
*
y
*
is
alone on the left side.