What is the equation of the line that goes through #(3, -6)# and is parallel to the line #3x+y-10=0#?

1 Answer
Apr 13, 2017

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

Explanation:

Let us find the slope of the given line #3x+y-10=0#.

By subtracting 3x from and adding 10 to both sides,

#Rightarrow y=-3x+10#

So, the slope is #-3#.

To find an equation of the line, we need two pieces of information:

  1. A point on the line: #(x_1, y_1)=(3,-6)#
  2. The slope: #m=-3# (same as the given line)

By Point-Slope Form #y-y_1=m(x-x_1)#,

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

This can be simplified to give

Slope -intercept form: #" "y = -3x+3#

Or standard form: #" "3x+y =3#

I hope that this was clear.