What is the equation of the line that is perpendicular to the given line and passes through the point (5, 3)? explain how you get your answer.

4x - 5y = 5
5x + 4y = 37
4x + 5y = 5
5x - 4y = 8

The equation for the graph of the picture is 

y = -5/4x

The slope of the perpendicular line needs to be the reciprocal of the other. To get reciprocal, switch the numerator and denominator with each other and flip the sign.

-5/4 ⇒ 4/-5 ⇒ 4/+5, or 4/5.

y = 4/5x + b

Input the coordinate point values and solve for b.

3 = 4/5(5) + b
Simplify.
3 = 4 + b
Subtract 4 from both sides.
-1 = b

y = 4/5x - 1

Now, we must convert this into Standard Form. It cannot contain any fractions and A, or the first number, cannot be negative.

y = 4/5x - 1
Subtract 4/5x from both sides.
-4/5x + y = -1
Multiply everything by -5 to make A positive and a whole number.
4x - 5y = 5

The first option is correct.

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