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Equation of line in standard form

Mike

New member
Jan 8, 2013
1
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

Administrator
Staff member
Jan 26, 2012
4,043
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! (Wave)

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

Administrator
Staff member
Feb 24, 2012
13,775
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:

$\displaystyle Ax+By=C$?