Friday, May 21, 2010

I need help with this maths question. How do I find the equation of this line in the form: ax + by + c=o?

The line passes through (-2,-3) and (1,4)

I need help with this maths question. How do I find the equation of this line in the form: ax + by + c=o?
(-2,-3) and (1,4)





slope m= y2-y1/(x2-x1)


m = 4-(-3)/(1-(-2)


m=7/3





y = mx + b


y = 7/3 x + b





compute c





c = y- 7x/3





c= 4 - 7(1)/3





c = 5/3





7/3 x + by + 5/3 = 0





multiply by 3





7x + 3y + 5 = 0
Reply:hello!


since both points lie on the same line, they both have to satisfy the equation:


-2a - 3b + c = 0


a + 4b + c = 0.


multiply the second equation by -2:


-2a - 8b - 2c = 0.





so you have:


-2a - 3b + c = 0


-2a - 8b - 2c = 0.





subtract the second equation from the first equation:


-2a - 3b + c = 0


- (-2a - 8b - 2c = 0)





and you get:


5b + c = 0.





subtract 5b from both sides to solve for c:


c = -5b





now substitute -5b for c in the original second equation, which was a + 4b + c = 0:


a + 4b - 5b = 0.





this can be simplified to:


a - b = 0, or


a = b.





thus the equation ax + by + c = 0 can be written:


bx + by - 5b = 0.





divide both sides by b:


x + y - 5 = 0, or x + y = 5.





and there you go! hope that wasn't too confusing- it's hard to explain via internet.
Reply:The equation of the (unique) line passing through two points whose coordinates are, respectively, (x₁,y₁) (x₂,y₂) is:


y - y₁= [(y₂- y₁) /(x₂- x₁)] (x - x₁) that in this circumstance is:


y - (-3) = [4 - (-3)] / [(1 - (-2)] [x -(- 2)] →


y + 3 = [(4 + 3) / (1 + 2)] (x + 2)


y + 3 = (7/ 3) (x + 2) in which by multiplying all terms by 3 you've


3y + 9 = 7(x + 2) → 3y + 9 = 7x + 14


and shifting terms to the right: 7x - 3y + 14 - 9 = 0 →


7x - 3y + 5 = 0 here's the equation in your required form





Bye!
Reply:you may use the two point gradient equasion form of a line:





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





just sub in the numbers and solve..





OR u could do it the long way...





find the gradient (rise/run)... (y1+y2)/(x1+x2)





then use a point/gradient formular: y-y1 = m(x-x1)





then u have the equasion of the line.. simple :D





note. the answer above may set it out for you (doing your homework) but my answer TEACHES you how to do it, and perform further questions of similar nature.





plz pick me for top answer :D:D:D::DD


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