find the equation of the line through (1,3) and (4,6). Write the equation in form:Ax+By=c?

Answer 1

First find the equation in the form y = mx + b
then manipulate it to get the form you want.

Next find the slope (m) :

m = (y" - y')/(x" - x') provided that x" - x' does not equal zero.

In this case m = (6-3)/(4-1) = 1

So y = 1x + b
Now Solve for b:

y = 1x + b implies:

1) 6 = 1(4) + b
2) 3 = 1(1) + b

Solve for b using either equation, double-check using the other equation, then manipulate the equation to get the form you want. The rest is left for the student.

Answer 2

To make it easier and make you enjoy the fun of Math let us begin with the general and known formula which is:
y = mx + b. Now as you can see whoever asked this question made a little modification and treated this general formula like this: -mx + y = b.
His/her A, B and C are our m, y and b respectively.

Let's begin solving it using the simplest way:
First we determine m = (y2 - y1)/(x2 - x1)
From our coordinates we can name them using this letters and numbers which I just wrote down.
Let
x1 = 1
y1= 3

x2 = 4
y2 = 6

We therefore subsitute these values in m = (6-3)/(4-1)=3/3=1and
We now have our m=A=1 and the general formula becomes y=x+b.
To get rid of b you can pick either (x1,y1) or (x2,y2) and substitute in the general formula which we have so far.
Let's pick (x1,y1) and we get 3=1+b
3-1=b
2=b and as above-mentioned b=c=2
Therefore the general formula keeps changing to y=x+2
Finally by rearranging this answer into the asked format we get
-x+y=2 which is the final answer.
Well this is it and may God bless you.

Answer 3

The equation to this line is (y-3)/(x-1) = (6-3)/(4-1) = 3/3 = 1

or y-3 = x-1
or x-y = -2 this is of the form Ax + By = c

Answer 4

the line will has same gradient as that which pases through 0,0 and 3,3 which is 1.
equation is thus 1x -1 y = 1-3 = 2.