How do you find the important points to graph $6 x y = 13$ $6xy = 13$ ?

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How do you find the important points to graph $6 x y = 13$ $6xy = 13$ ?

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Answer 1 · 2016-02-08T09:28:43

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

Explanation:

Using the given $6 x y = 13$ $6xy=13$

use $y = \frac{13}{6 x}$ $y=13/(6x)$

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

when $x =$ $x=$ approaches $\infty$ $oo$ , $y =$ $y =$ approaches $0$ $0$ that is why $y = 0$ $y=0$ is an asymptote

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

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

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

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How do you find the important points to graph $6 x y = 13$ $6xy = 13$ ?

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Explanation:

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