anonymous
  • anonymous
Write the equation of the line that passes through the points (3,2) and (2,3)
Mathematics
chestercat
  • chestercat
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pooja195
  • pooja195
First we need to find the slope
pooja195
  • pooja195
\[\huge~\rm~\frac{ y_2-y_1 }{ x_2-x_1 }=slope\]
anonymous
  • anonymous
1/-1

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pooja195
  • pooja195
Or in other words just -1 what form do they want the equation in?
anonymous
  • anonymous
y=mx+b
pooja195
  • pooja195
oh ok so now we use the point slope equation \[\huge~\rm~y-y_1=m(x-x_1)\] (x1,y1)=(3,2) m=slope which is -1 just plug in the given information and solve for y
anonymous
  • anonymous
what would x be?
texaschic101
  • texaschic101
or you can use y = mx + b...either formula will work
pooja195
  • pooja195
x and y are just there they help to figure out the slope and the equation
pooja195
  • pooja195
or you can use @texaschic101 's method
texaschic101
  • texaschic101
and you x and y points.....you can use either set (3,2) or (2,3)
texaschic101
  • texaschic101
which formula do you want to proceed with ?
anonymous
  • anonymous
y=-3+b... im stuck\
anonymous
  • anonymous
y=mx+b (3,2)
texaschic101
  • texaschic101
you forgot about your slope(m) of -1
anonymous
  • anonymous
i did -1(3)
texaschic101
  • texaschic101
y = mx + b slope(m) = -1 (3,2)...x = 3 and y = 2 now we sub 2 = -1(3) + b 2 = -3 + b -- add 3 to both sides 2 + 3 = b 5 = b so your line is : y = -1x + 5 or just y = -x + 5 but if you sub in your other set of points..(2,3) 3 = -1(2) + b 3 = -2 + b 3 + 2 = b 5 = b same thing....y = -x + 5 so either of your points will give you this answer
texaschic101
  • texaschic101
questions ?
texaschic101
  • texaschic101
now if they wanted the answer is point-slope form you would use : y - y1 = m(x - x1). You could also use it for this problem but you would eventually have to change it to y = mx + b form
anonymous
  • anonymous
no that explains it.
texaschic101
  • texaschic101
glad to help...but please give medal to pooja195....I kinda took over her explaining...should not have done that.

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