How do you write the equation of the line through the given points in standard form: (0,7) (-5,12)?

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How do you write the equation of the line through the given points in standard form: (0,7) (-5,12)?

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Answer 1 · 2015-04-03T01:40:13

For a straight line the slope between any two points on the line is the same no matter which two point you choose.

If $(x_{1}, y_{1})$ $(x_1,y_1)$ and $(x_{2}, y_{2})$ $(x_2,y_2)$ are two points on a line then the slope is given by
$\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $(y_2-y_1)/(x_2-x_1)$

Consider a general (variable) point on the desired line: $(x, y)$ $(x,y)$ plus the two given points. Remembering that the slope is always equal no matter which two points you choose:

$\frac{y - 7}{x - 0} = \frac{12 - 7}{(- 5) - 0}$ $(y-7)/(x-0) = (12-7)/((-5)-0)$

Simplifying we have
$y - 7 = \frac{5 x}{- 5}$ $y-7 = (5x)/(-5)$
or
$y = 7 - x$ $y = 7-x$

Depending upon your definition of "standard form" this might be expressed as
$x + y = 7$ $x+y = 7$

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How do you write the equation of the line through the given points in standard form: (0,7) (-5,12)?

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