Pointslope Form for the Equation of a Line
We can find the equation of a line if we know the slope of the line, m, and
a point on the line, (x_{1}, y_{1}). Hereâ€™s how we can derive a formula for this.
Start with the formula for the slope of a line that
passes through the points, (x_{1}, y_{1}), and (x_{2}, y_{2}). 
m 

Replace (x_{2}, y_{2}) with (x, y). 
m 

Multiply both sides by x  x_{1}. 
m(x  x_{1}) 

Simplify the right side. 
m(x  x_{1}) 
= y  y_{1} 
By tradition, the y terms are written on the left. 
y  y_{1} 
= m(x  x_{1}) 
The result is called the pointslope form for the equation of a line.
Note:
(x_{1}, y_{1}) represents a point on the line that
we know.
(x, y) represents an unknown point on the
line.
Definition
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}) and has slope m is.
y  y_{1} = m(x  x_{1})
Note that m, x_{1}, and y_{1} are constants, and x and y are variables.
The following linear equations are written in pointslope form:

Here, (x_{1}, y_{1}) = (4, 7) and

y  2 = 3(x  1) 
Here, (x_{1}, y_{1}) = (1, 2) and m = 3. 
