# find the equation of the line passing through points (2,4) and (3,2)?

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• First find the gradient (m)

m = [2 - 4]/{3-2] = -2/1 = -2

Displace (x,y) against any one point and using the gradient.

y - 4 = -2(x - 2)

y - 4 = -2x + 4

y = -2x + 8

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• Gradient => (2 - 4)/(3 - 2) = -2

so, equation is y = -2x + c

Using point (2, 4) we have:

4 = -2(2) + c

i.e. c = 8

Hence, y = -2x + 8

or, y + 2x - 8 = 0

:)>

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• Point A: Ax = 2, Ay = 4; Point B: Bx = 3, By = 2.

Two-point form: (y - By)/(Ay - By) = (x - Bx)/(Ax - Bx).

Hence: (y - 2)/(4 - 2) = (x - 3)/(2 - 3) => (y - 2)/2 = (x - 3)/(-1) => (y - 2)/2 = 3 - x =>

=> y - 2 = 2(3 - x) => y - 2 = 6 - 2x => y = -2x + 6 + 2 => ANSWER: y = -2x + 8.

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• Equation of the straight line (two-point form) :

(y - 4)/(x - 2) = (2 - 4)/(3 - 2)

(y - 4)/(x - 2) = -2

y - 4 = -2(x - 2)

y - 4 = -2x + 4

2x + y - 8 = 0

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