PointSlope 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 pointslope form.
It displays the coordinates of a point, (2, 5), and the slope,
.
We can easily write the equation of a line in pointslope form when we are
given the coordinates of a point on the line and the slope of the line.
Definition â€”
PointSlope Form for the Equation of a Line
The pointslope form for the equation of a line that passes through
the point (x_{1}, y_{1}) with slope m is:
y  y_{1} = m(x  x_{1})
Note that m, x_{1}, and y_{1} 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 pointslope form.
Solution
Here is the pointslope form for the
equation of a line. The slope, m, is 3. So, replace m with 3.
A point, (x_{1}, y_{1}), on the line is (7, 4).
So, replace x_{1} with 7, and replace y_{1} with 4. 
y  y_{1}
y  y_{1}
y  (4) 
= m(x  x_{1})
= 3(x  x_{1})
= 3(x  7) 
The equation of the line in pointslope form
is y  (4) = 3(x  7).Note:
You can simplify the left side of the
equation to obtain
y + 4 = 3(x  7).
