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
5x = 10y – 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, x1 =
5, and y1 = –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.
