Reading on how to check for symmetry, book uses this equation $\displaystyle y=x^3$. I am asked to do the same but with this equation;

$\displaystyle y=-5x$

I want to know if I did right or done something wrong...

In looking for points to plot I did the following:

X___Y

0___0

1___-5

2___-10

-1___5

-2___10

Now, about checking these points for symmetry. If I was to check for the y Axis I would have to replace x by -x, so then the equation would look like this;

$\displaystyle y=-5-x$correct?

So my Y axis ends up being positive $\displaystyle y=-5(-1)$ = $\displaystyle y=5$right?

And if checking for the x Axis I would replace y by -y, $\displaystyle -y=-5x$

so now my y axis remains a negative thus giving me this;

$\displaystyle -y=-5(1)$ = $\displaystyle y=-5$so far correct?

So for this equation y=-5x, we can say that it is only symmetric with respect to the origin, yes?!

Thanks for taking the time on this!