What is the equation of the line between #(-7,2)# and #(7,-38)#?

1 Answer
Jun 25, 2018

Slope-intercept form: #y=-20/7 x-18#
Standard form: #20x+7y=-126#

Explanation:

I will assume that you want the equation in slope-intercept form. Here, we can use the format for finding the slope given two points, which is

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

In our problem #(x_1,y_1)# is #(-7,2)# and #(x_2,y_2)# #(7,-38)#. We can insert values and find the slope:

#(-38-2)/(7-(-7))=-40/(7+7)=-40/14=-20/7#

Next, we choose one of our coordinates and put that into the formula for a line in slope-intercept form,

#y=mx+b#

Let's choose #(-7,2)#:

#2=-20/7(-7)+b#
#2=20+b#
#-18=b#

This gives us our final equation, #y=-20/7 x-18#.

If you needed standard form, here's how we can do that:

#20/7 x+y=-18#
#7*(20/7 x+y)=(-18)*7#
#20x+7y=-126#

Hope this helps!