# Equation of line in standard form

#### Mike

##### New member
I am having trouble with algebra... I have to write an equation in standard form containing the given point and having the give slope for (2,1);m=1

I have no clue what I am doing and am not able to find anything online. Please help

#### Jameson

Staff member
I am having trouble with algebra... I have to write an equation in standard form containing the given point and having the give slope for (2,1);m=1

I have no clue what I am doing and am not able to find anything online. Please help
Hi Mike,

Welcome to MHB!

There is something called the "point-slope" form of a line. It looks like this. $$\displaystyle y-y_0=m(x-x_0)$$. $m$ is the slope and the $x_0$ and $y_0$ refer to a point $(x_0,y_0)$.

If we plug in your info we get $$\displaystyle y-1=1(x-2)$$. Can you rearrange that and put it into standard form?

Jameson

#### MarkFL

Staff member
Hello and welcome, Mike!

Let $\displaystyle (x,y)$ be a general point on the line (other than the given point (1,2)). Using the definition of slope, we may write:

$\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{y-1}{x-2}=1$

Note: using the point-slope formula will give us the same result, and more quickly (and once you are familiar with this formula, it is the way to go here), but I wanted to show you an alternate route, and if you think about it, you can see that this is a way to actually derive the point-slope formula.

$\displaystyle \frac{y-1}{x-2}=1$

Now, what should you do first to try to get this into the form:

$\displaystyle Ax+By=C$?