What is the equation of the line that goes through #(- 5,4)# and #( 2,8)#?

1 Answer
May 12, 2018

#y=4/7x+48/7#

Explanation:

The line is probably linear, and so it is given by:

#y=mx+b#

  • #m# is the slope of the line

  • #b# is the y-intercept

The slope #m# is found by:

#m=(y_2-y_1)/(x_2-x_1)#, where #(x_1,y_1)# and #(x_2,y_2)# are the two coordinates.

So here:

#m=(8-4)/(2-(-5))#

#=4/7#

So, the equation is:

#y=4/7x+b#

Now, we plug in any of the two coordinates' #x# and #y# values into the equation, and we will get the #b# value. I'll choose the first coordinate.

#:.4=4/7*-5+b#

#4=-20/7+b#

#b=4+20/7#

#=48/7#

#:.y=4/7x+48/7#

Trying for the second coordinate:

#8=4/7*2+48/7#

#8=8/7+48/7#

#8=56/7#

#8=8# (CORRECT!)

Indeed, the line is #y=4/7x+48/7#. Here is its graph:

graph{4/7x+48/7 [-10, 10, -5, 5]}