I was told to "Find the equation of the line that is equadistant from points (2,6) and (8,4)" And i was told to write it in standard y=mx+b form

I came to the conclusion of y=1x+0 But it gets marked as wrong. What am i missing?

Elijah Apr 19, 2022

#5**+1 **

Heres how to solve it:

Connecting both the points, we find that the line has a slope of \(-{1 \over 3}\)

Because we want the line to be equidistant, it needs to be perpendicular with this "imaginary" line, meaning the slope is 3.

The line will also have to go through the point that is halfway from \((2, 6)\) and \((8,4)\). This point is \((5,5)\).

We have the form \(y=3x+b\)

Subsituting the point we have, we find that \(b=-10\)

Putting the equation together, we have \(\color{brown}\boxed{y=3x-10}\)

BuilderBoi Apr 19, 2022