What is the equation of the line passing through $(8,2), (5,8)$ ?

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Answer 1 · 2016-01-04T17:26:35

In general form:

$2x+y-18 = 0$

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the equation:

$m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1)$

Let $(x_1, y_1) = (8, 2)$ and $(x_2, y_2) = (5, 8)$

Then:

$m = (8-2)/(5-8) = 6/(-3) = -2$

The equation of the line passing through $(8, 2)$ and $(5, 8)$ can be written in point slope form as:

$y - y_1 = m(x-x_1)$

That is:

$y - 2 = -2(x - 8)$

Add $2$ to both sides to find:

$y = -2x+18$

which is the slope intercept form of the equation of the line.

Then putting all terms on one side by adding $2x-18$ to both sides we find:

$2x+y-18 = 0$

which is the general form of the equation of a line.

What is the equation of the line passing through (8,2), (5,8)(8,2), (5,8)?