Pointslope Form for the Equation of a Line
Example 1
Find the equation of the line that passes through the point (4, 7) with
slope
.
Solution
Use the pointslope formula.

y  y_{1} 
= m(x  x_{1}) 
We are given the point (4, 7),
so let x_{1} = 4 and y_{1} = 7. 
y  7 
= m(x  (4)) 
The slope is
. 
y  7 

Simplify the right side. 
y  7 

So, the equation of the line is


Example 2
Find the equation of the line that passes through the points (3, 3) and (6,
1).
Solution
First, find the slope of the line.



Let (x_{1}, y_{1}) = (3, 3) and
(x_{2}, y_{2}) = (6, 1). 


Next, use the pointslope formula.

y  y_{1} 
= m(x  x_{1}) 
We can use either given point.
Letâ€™s use (6, 1). 
y  (1) 

Simplify the left side. 
y + 1 

So, the equation of the line is



Note:
If we had used the other point, (3, 3), we would have obtained:
y  y_{1} 
= m(x  x_{1}) 
y  (3) 

y + 3 

This equation is equivalent to
since both simplify to
.
