equation of a line

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HNO

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1. Find the equation of a line which goes through A(2,3) and B(4,-6). State your answer in general form

Again my teacher decides to put a question on our assignment that has nothing to do with our unit right now. So I need some refreshment.

I know how to find slope x1-y1 / x2-y2 ( I think thats write)

so that would be 2-4= -2
3- (-6)= 9

-2/9 *** Slope?

General form is ax + by + c =0

is it now -2/9 + by + c = 0 ??

Help is appreciated :D

Tomorrow my assignment is due, and this was the last question that I have been trying to figure out…
 
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HNO said:
1. Find the equation of a line which goes through A(2,3) and B(4,-6). State your answer in general form

Again my teacher decides to put a question on our assignment that has nothing to do with our unit right now. So I need some refreshment.

I know how to find slope x1-y1 / x2-y2 ( I think thats write)

so that would be 2-4= -2
3- (-6)= 9

-2/9 *** Slope? ..................Incorrect

Slope of a line (m) passing through to points (x1, y1) and (x2, y2) is:

m = (y2 - y1) / (x2 - x1)
Thus in your case slope is:

m = (-6 -3)/(4-2) = - 9/2


General form is ax + by + c =0

is it now -2/9 + by + c = 0 ??

Help is appreciated :D

Tomorrow my assignment is due, and this was the last question that I have been trying to figure out…
Click to expand...

Find the equation of a line which goes through A(2,3) and B(4,-6).

Equation of a line (m) passing through to points (x1, y1) and (x2, y2) is:

(y - y1) / (y2 - y1) = (x - x1) / (x2 - x1)

In your case:

[y - 3]/[(-6) - (3)] = [x - 2]/ [4 - 2]

Now simplify and rearrange to present in the required form.
 
Subhotosh Khan said:
Find the equation of a line which goes through A(2,3) and B(4,-6).

Equation of a line (m) passing through to points (x1, y1) and (x2, y2) is:

(y - y1) / (y2 - y1) = (x - x1) / (x2 - x1)

In your case:

[y - 3]/[(-6) - (3)] = [x - 2]/ [4 - 2]

Now simplify and rearrange to present in the required form.
Click to expand...

THANK YOU SO MUCH … You have been a great help (=
 
Another way to do this: any (non-vertical) line can be written in the form y= mx+ b. In order that it pass through (2,3), we must have 3= 2m+ b and in order that it pass through (4,-6), we must have -6= 4m+ b. That gives two equations to solve for a and b. One obvious way to start is to eliminate b by subtracting one equation from another. When you do that, and solve for m, you will be doing exactly the same thing as using the formula for slope.
 
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