How do you write an equation of a line with points (-2,5), (5,-2)?

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How do you write an equation of a line with points (-2,5), (5,-2)?

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Answer 1 · 2017-01-18T17:24:12

#y = -x +3#

Explanation:

A line is given by the equation #y - y_0 = m(x-x_0)# where #m# is the slope of the line, and #(x_0,y_0)# a point on the line. To find the slope of a line when two of its points - #(x_1,y_1)# and #(x_2,y_2)# are known, use the formula:

#m = (y_2-y_1)/(x_2-x_1)#

In this case, #m = (-2 - 5)/(5 - (-2)) = -7/7 = -1#.

Let's use the point #(x_1,y_1)# as the point #(x_0, y_0)# from the first equation:

#y - 5 = -1(x-(-2)) => y = -x -2 + 5 => y = -x +3#

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How do you write an equation of a line with points (-2,5), (5,-2)?

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