Point-Slope Form for the Equation of a Line
Suppose we want to find the equation of the line that passes through the
point (2, 5) with slope
 .
This equation of the line is in point-slope form.
It displays the coordinates of a point, (2, 5), and the slope,
.
We can easily write the equation of a line in point-slope form when we are
given the coordinates of a point on the line and the slope of the line.
Definition —
Point-Slope Form for the Equation of a Line
The point-slope form for the equation of a line that passes through
the point (x1, y1) with slope m is:
y - y1 = m(x - x1)
Note that m, x1, and y1 are constants, whereas x and y are variables.
Example
Find the equation of the line that passes through the point (7, -4) with
slope 3.
Write your answer in point-slope form.
Solution
| Here is the point-slope form for the
equation of a line. The slope, m, is 3. So, replace m with 3.
A point, (x1, y1), on the line is (7, -4).
So, replace x1 with 7, and replace y1 with -4. |
y - y1
y - y1
y - (-4) |
= m(x - x1)
= 3(x - x1)
= 3(x - 7) |
The equation of the line in point-slope form
is y - (-4) = 3(x - 7).Note:
You can simplify the left side of the
equation to obtain
y + 4 = 3(x - 7).
|
