How do you write the equation of a line in point slope form and slope intercept form given points (3, -8) (-2, 5)?

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Answer 1 · 2015-05-27T11:56:47

Given the points #(3,-8)# and #(-2,5)#
both the point-slope form and the slope-intercept form require that we first determine the slope.

The slope can be calculated as
#m = (Delta y)/(Delta x) = (5-(-8))/(-2-3) = - 13/5#

Using the slope #m=-13/5# and the point #(3,-8)#
the slope-point form (#y-y_1 = m(x-x_1)#) is

#y-(-8) = -13/5(x-3)#
or
#y+8 = -13/5(x-3)#

The slope-point form can be converted into the slope-intercept form (#y=mx+b#) by some minor re-arranging of terms:
#y+8 = -13/5(x-3)#

#rarr y = -13/5 x +39/5 -8#

#rarr y = -13/5x -1/8#