What is the equation of the line that contains the points with (x, y) coordinates (-3, 7) and (5, -1)?

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Answer 1 · 2015-05-25T19:03:58

First calculate the slope, which is (change in y) / (change in x)...

slope $= (Delta y)/(Delta x) = (-1 - 7) / (5 - (-3)) = -8/8 = -1$

The line can now be expressed in point slope form

$y - y_0 = m(x - x_0)$

where $m$ is the slope and $(x_0, y_0)$ is a point on the line:

$y - 7 = (-1)(x - (-3))$

To convert to slope intercept form, add $7$ to both sides to get:

$y = (-1)(x - (-3)) + 7$
$= -(x+3) + 7$
$= -x -3 + 7$
$= -x+4$

$y = -x + 4$ is in the form $y = mx + c$ , with slope $m = -1$ and intercept $c = 4$ .