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Am I correct?

So I need to make a perpendicular line through the -2,3 point.
How can I do that?

it is simple the slope of the requested line, is:
\[\large m = - \frac{1}{5}\]

I have the slope intercept form for -2,3 as y=5x + 2

so you have to apply this equation:
\[\large y - 3 = - \frac{1}{5}\left( {x + 2} \right)\]

So now do I need to do: -1/5x + 2= y?

Is your and my equations the same thing? @Michele_Laino

Would that line work?

My line doesn't work. It is not perpendicular.

I think not, since that line is not perpendicular to both the parallel lines

please try with this line:
\[\large y = - \frac{x}{5} + \frac{{13}}{5}\]

@Michele_Laino How did you get 13/5?

I am really sorry fir being redundant. :(

*for

hint:
\[ \Large - \frac{2}{5} + 3 = \frac{{ - 2 + \left( {3 \times 5} \right)}}{5} = ...?\]

How did you get -2+(3 x 5)?

Oh okay!!!!! I totally get it now :)

So for x I can input any number now?