What is the equation of the line passing through #(4,8)# and #(-9,3)#?

Method 1:
Use point slope form
which is #y - y_1 = m(x - x_1)#
when given a point #(x_1, y_1)# and the slope #m#
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In this case, we should first find the slope between the two given points.
This is given by the equation:
#m = frac{y_2 - y_1}{x_2 - x_1}#
when given the points #(x_1,y_1)# and #(x_2, y_2)#
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For #(x_1,y_1) = (4,8)# and #(x_2,y_2) = (-9,3)#
By plugging what we know into the slope equation, we can get:
#m = frac{3-8}{-9-4} = frac{-5}{-13} = frac{5}{13}#
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from here we can plug in either point and get:
#y - 8 = frac{5}{13}(x-4)#
or
#y - 3 = frac{5}{13}(x+9)#

Method 2:
Use slope intercept form
which is #y = mx + b#
when #m# is the slope and #b# is the y-intercept
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We can find the slope between the two given points using the same steps as above
and get #m= frac{5}{13}#
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but this time when we plug in, we will still be missing the #b# or y-intercept
to find the y-intercept, we need to temporarily plug in one of the given points in for #(x,y)# and solve for b
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so
#y= frac{5}{13}x + b#
if we plug in #(x,y)=(4,8)#
we would get:
#8 = frac(5)(13)(4) + b#
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solving for #b# would get us
#8 = frac{20}{13} + b#
#b = 84/13 or 6 frac(6)(13)#
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so your equation would be
#y = frac(5)(13)x + frac(84)(13)#

another form your equation could be in can be standard form where only the variables are on one side
#ax + by = c#
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you can get you equation into this form by multiplying both sides of the slope intercept equation by 13
to get #13y = 5x + 84#
then subtract #5x# from both sides
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so your standard form equation would be
#-5x + 13y = 84#