How do you write the equation of a line with points (-8,14), (-20,17)?

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Answer 1 · 2016-12-13T22:08:54

$y - 14 = -1/4(x + 8) or$ y = -1/4x + 12#

To find the equation for these two points we must first determine the slope of the line.

The slope can be found by using the formula:

$color(red)(m = (y_2 = y_1)/(x_2 - x_1)$

Where $m$ is the slope and $(x_1, y_1)$ and $(x_2, y_2)$ are the two points.

Substituting the points we are give allows us to calculate the slope as:

$m = (17 - 14)/(-20 - -8)$

$m = 3/(-20 + 8)$

$m = -3/12$

$m = (3/3) xx (-1/4)$

$m = 1 xx (-1/4)$

$m = -1/4$

Now, we can use the point-slope formula to find the equation for the line. The point-slope formula states:

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

Where $m$ is the slope and #(x_1, y_1) is a point the line passes through.

We can substitute the slope we calculated earlier and one of the points to obtain our equation for the line:

$y - 14 = -1/4(x - -8)$

#y - 14 = -1/4(x + 8)

Or solving for $y$ to put the equation into slope intercept form gives:

$y - 14 = -1/4x + -1/4 xx 8$

$y - 14 = -1/4 x - 8/4$

$y - 14 = -1/4x - 2$

$y - 14 + 14 = -1/4x - 2 + 14$

$y - 0 = -1/4x + 12$

$y = -1/4x + 12$