Parallel and perpendicular. rewriting equations in standard form?

Question

I have the answers in the back of the book.

because they are odd questions for this homework assignment.

I need some help on

# 23 -4x-9y= -23 ; (12, -15)

Im supposed to write the standarf form of the equation of the line that is parallel to the graph of the given equstion and passes through the point with the giver coordinates..

im not to sure how to do that question

Can you use words to explain my steps PLEASE?

and I need help on

#27 - x=12 ; (6, -13)

thank you in advance for being so kind :)

Answer 1

-4x-9y= -23

Rearrange it in y = mx + b form to find your slope, m.  Since you want a parallel line's equation, that must mean the slopes are EQUAL.

Solve for the other equation using again y = mx + b, since you have m, and x/y from the given coordinates --> solve for b.  Then rewrite the equation.

For your other question, do you mean

-x = 12?

x = -12

This is clearly not a function, since the slope is undefined.  However, if you wanted a line parallel to this like the first question, obviously, the point would be x = 6, making both lines perfectly horizontal with one answer.  Try drawing it out if you can't see it right away.

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