What is the equation of the line passing through #(-5,4)# and #(9,-4)#?

1 Answer
Mr. Raj
Jun 12, 2017

#y=-4/7x+8/7#
or #4x+7y=8#

Explanation:

First up, it's a line, not a curve, so a linear equation. The easiest way to do this (in my view) is using the slope intercept formula which is #y=mx+c#, where #m# is the slope (the gradient) of the line, and c is the y-intercept.

The first step is the calculate the slope:
If the two points are #(x_1, y_1)" and "(x_2, y_2)#, then

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

#=>m=(-4-4)/(9-(-5))#

#=>m=(-4-4)/(9+5)#

#=>m=-8/14#

#=>m=-4/7#

So we now know a bit of the equation:

#y=-4/7x+c#

To find #c#, substitute in the values for #x# and #y# from any one of the two points, so using #(-5,4)#

#(4)=-4/7(-5)+c#

And solve for c

#=>4=(-4*-5)/7+c#

#=>4=20/7+c#

#=>4-20/7=c#

#=>(4*7)/7-20/7=c#

#=>28/7-20/7=c#

#=>8/7=c#

Then put in #c# and you get:

#y=-4/7x+8/7#

If you want, you can rearrange this into the general form:

#=>y=1/7(-4x+8)#

#=>7y=-4x+8#

#4x+7y=8#

And your graph would look like:
graph{4x+7y=8 [-18.58, 21.42, -9.56, 10.44]}

(you can click and drag on the line until you get the points if you want to double check)

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