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.
