Question

How do you find the important points to graph `6xy = 13`?

Answer 1

The graph occupies the 1st and 3rd quadrants only. The asymptotes are the x-axis and y-axis. Calculate y values using x values `+-0.25` up to `+-4`

Explanation:

Using the given `6xy=13`

use `y=13/(6x)`

when `x=+0.25` , `y=+8.66`
when `x=+0.5` , `y=+4.33`
when `x=+1` , `y=+2.166`
when `x=+2` , `y=+1.083`
when `x=+3` , `y=+0.722`
when `x=+4` , `y=+0.25`

when `x=`approaches `oo`, `y =`approaches `0` that is why `y=0` is an asymptote

at the very high + value of `y` , `x` approaches 0
also
at the very negative value of `y` , `x` approaches 0,
that is why `x=0` is also an asymptote

when `x=-0.25` , `y=-8.66`
when `x=-0.5` , `y=-4.33`
when `x=-1` , `y=-2.166`
when `x=-2` , `y=-1.083`
when `x=-3` , `y=-0.722`
when `x=-4` , `y=-0.25`

graph{y=13/(6x)[-20,20,-10,10]}

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