How do you write an equation of a line given (3, 5) and (-6, -1)?

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Answer 1 · 2017-08-14T07:50:12

Find the gradient and the #y#-intercept in #y = mx + c # to get

#3y = 2x + 9#

#y=mx+c# is the slope-intercept equation of any straight line. So we need to find #m#, the gradient of the line, and #c#, the #y#-intercept.

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

#y_2# being the second #y# value, which is #-1#, and #y_1# is #5#. The same goes for #x_2# and #x_1#, so

#m = ( -1 - 5 ) / (-6-3)#

#m = (-6)/-9 = 2/3#

Since

#y = mx+c#

to find #c# do

#c = y - mx#

We substitute one of the coordinates, for eg. #( 3 , 5 )#, so

#c = 5 - (2/3)*3#

#c = 3#

Therefore, we substitute the values of #m# and #c# in #y = mx + c#
to get

#y = 2/3x+3#

#3y = 2x + 9#