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What is the equation of the line passing through (1, f(1)) and (3, f(3)) if f(x) = 3x^2...

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xetatheta | Student, Kindergarten | Salutatorian

Posted February 15, 2013 at 6:04 PM via web

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What is the equation of the line passing through (1, f(1)) and (3, f(3)) if f(x) = 3x^2 + 1

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 15, 2013 at 6:11 PM (Answer #1)

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The function f(x) = 3x^2 + 1. This gives the coordinates of the points (1, f(1)) and (3, f(3)) as (1, 3*1 + 1) and (3, 3*3^2 + 1) or (1, 4) and (3, 28) resp.

The equation of the line passing through points `(x_1, y_1)` and `(x_2, y_2)` is `(y- y_1)/(x - x_1) = (y_2 - y_1)/(x_2 - x_1)` . Substituting the coordinates of the points the equation of the line is:

`(y- 4)/(x - 1) = (28 - 4)/(3 - 1)`

=> `(y- 4)/(x - 1) = 12`

=> y - 4 = 12x - 12

=> 12x - y - 8 = 0

The required equation of the line is 12x - y - 8 = 0

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