PointSlope Equation of a Line
The "pointslope" form of the equation of a straight line is:
y  y_{1} = m(x  x_{1})
Using this formula, when we know:
we can find other points on the line.
What does it stand for?
(x_{1}, y_{1}) is a known point
m is the slope of the line
(x, y) is any other point on the line
Making Sense of It
It is based on the slope:
Slope m =  change in y  =  y  y_{1} 
change in x  x  x_{1} 
So this is the slope: and we can rearrange it like this:
to get this: 
So, it is just the slope formula in a different way!
Now let us see how to use it.
Example 1
slope "m"  = 

= 3 
y  y_{1} = m(x  x_{1})
We know m now, and also know that (x_{1}, y_{1}) = (3,2), and so we have:
y  2_{} = 3(x  3_{})
That is a perfectly good answer, but we can simplify it a little:
y  2_{} = 3x  9
y_{} = 3x  9 + 2
y_{} = 3x  7
Example 2
slope "m"  = 

= 3 
y  y_{1} = m(x  x_{1})
We can pick any point for (x_{1}, y_{1}), so let's choose (0,0), and so we have:
y  0_{} = 3(x  0_{})
Which can be simplified to:
y _{} = 3x
Example 3: Vertical Line
What is the equation for a vertical line?
The slope is undefined!
In fact, this is a special case, and we use a different equation, like this:
x = 1.5 
Every point on the line has x coordinate 1.5,
thatâ€™s why its equation is x = 1.5
What About y = mx + b ?
You may already be familiar with the "y=mx+b" form.
It is the same equation, in a different form!
The "b" value (called the yintercept) is where the line crosses the yaxis.
So point (x_{1}, y_{1}) is actually at (0_{}, b_{})
and the equation becomes:
Start with  y  y_{1} = m(x  x_{1}) 
(x_{1}, y_{1}) is actually (0_{}, b_{}):  y  b_{} = m(x  0_{}) 
Which is:  y  b_{} = mx 
Put b on other side:  y_{} = mx + b 
And that is called the "slopeintercept" form of the equation of a line.