Distance between point and line in point slope form on a plane

If I have an equation in point slope form $$y=mx$$ how can I use the perpendicular distance formula:

$$\text{Perpendicular Distance} = \frac{\left | Ax_{1} + By_{1} + C\right |}{\sqrt{A^2 + B^2} }$$

with my equation in point slope form knowing that this formula is designed for standard form?

• The line eq. is generally $y=mx+c$ which you can write as $mx-y+c$ c.f. this with $Ax+Bc+C$, you will get your values. – chandresh Dec 11 '15 at 6:48

When given an equation in point slope form it is important to recognize that you can manipulate the equation to obtain values for A, B, and C and then use the perpendicular distance formula.

y=mx

subtract y from both sides in order to convert to standard form and get:

mx - y = 0.

Now you can determine your A, B, and C.

A=m; B=-1; C=0.

Convert to standard form.
$$y = mx$$

$$mx - y = 0$$

$$A = m; B = -1; C = 0$$

Then convert the equation to standard from. $y=mx$ is the same as $mx-y=0$ where $A=m$, $B=-1$, and $C=0$.