How do you write the equation in point slope form given (–2, 15), (9, –18)?

2 Answers
Feb 22, 2016

#y-15=-3(x+2)#

Explanation:

Slope:
#color(white)("XXX")m=(Delta y)/(Delta x) = (15-(-18))/(-2-9)=33/(-11) = -3#

The general slope-point form for a line with slope #m# through a point #(barx,bary)# is
#color(white)("XXX")y-bary=m(x-barx)#

Using #(-2,15)# for #(barx,bary)#
#color(white)("XXX")y-15=-3(x+2)#

Feb 22, 2016

Equation of the line is #3x+y=9#

Explanation:

Equation of the line between two points say #(x_1,y_1)# and #(x_2,y_2)# in point slope form is given by

#(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)#, where both LHS and RHS represent slope of the line,

Hence equation of the line between #(-2,15)# and #(9,-18)# is given by

#(y-15)/(x-(-2))=((-18)-15)/(9-(-2))# i.e.

#(y-15)/(x+2)=(-18-15)/(9+2)# or #(y-15)/(x+2)=(-33)/11=-3# i.e.

#(y-15)=-3*(x+2)# i.e.

#(y-15)=--3x-6#

or #3x+y=-6+15=9#

As such, equation of the line is #3x+y=9#