What is the equation of the line passing through $(11, 17)$ $(11,17)$ and $(23, 11)$ $(23,11)$ ?

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What is the equation of the line passing through $(11, 17)$ $(11,17)$ and $(23, 11)$ $(23,11)$ ?

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Answer 1 · 2015-11-18T13:24:20

$x + 2 y = 45$ $x+2y=45$

Explanation:

1st point $= (x_{1}, y_{1}) = (11, 17)$ $=(x_1, y_1)=(11, 17)$
2nd point $= (x_{2}, y_{2}) = (23, 11)$ $=(x_2, y_2)=(23, 11)$

First, we will have to find the slope $m$ $m$ of this line:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{11 - 17}{23 - 11} = - \frac{6}{12} = - \frac{1}{2}$ $m=(y_2-y_1)/(x_2-x_1)=(11-17)/(23-11)=-6/12=-1/2$

Now, use point-slope formula with one of the given points:
$y - y_{1} = m (x - x_{1})$ $y-y_1=m(x-x_1)$
$y - 17 = - \frac{1}{2} (x - 11)$ $y-17=-1/2(x-11)$
$y - 17 = - \frac{1}{2} x + \frac{11}{2}$ $y-17=-1/2x+11/2$
$y = - \frac{1}{2} x + \frac{11}{2} + 17$ $y=-1/2x+11/2+17$
$y = \frac{- x + 11 + 34}{2}$ $y=(-x+11+34)/2$
$2 y = - x + 45$ $2y=-x+45$
$x + 2 y = 45$ $x+2y=45$

Answer 2 · 2015-11-18T13:56:52

$y = - \frac{x}{2} + \frac{45}{2}$ $y = -x/2 + 45/2$

Explanation:

Usung the formula $y - y_{1} = m (x - x_{1})$ $y-y_1 = m(x-x_1)$
Considering
$(11, 17) and (23, 11)$ $(11, 17) and (23, 11)$
$(x_{1}, y_{1}) and (x_{2}, y_{2})$ $(x_1, y_1) and (x_2, y_2)$

m (gradient) = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $(y_2-y_1)/(x_2-x_1)$

m = $\frac{11 - 17}{23 - 11}$ $(11-17)/(23-11)$

m = $- \frac{6}{12}$ $-6/12$

m = $- \frac{1}{2}$ $-1/2$

$y - 17 = - \frac{1}{2} (x - 11)$ $y-17 = -1/2(x-11)$
$y - 17 = - \frac{x}{2} + \frac{11}{2}$ $y-17 = -x/2+11/2$
$y = - \frac{x}{2} + \frac{11}{2} + 17$ $y = -x/2+11/2+17$
$y = - \frac{x}{2} + \frac{45}{2}$ $y = -x/2 + 45/2$

This is the equation of the line

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What is the equation of the line passing through $(11, 17)$ $(11,17)$ and $(23, 11)$ $(23,11)$ ?

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