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#.