The given line is y = 3x - 5 after adding Y and subtracting 5 from both sides.
The slope of this given line is 3.
Therefore, the slope of the perpendicular line is -1/3, as it must be the negative reciprocal.
The general form of a line equation in slope intercept form is y = Mx+B where M is the slope and B is the intercept.
Solving for B is: B = y- Mx
So the intercept of the perpendicular line with slope M=-1/3 and passing through (x=4, y=-3) is
y M * x
B = -3 - (-1/3)*4 =
-3 + 1/3*4 = <-- subtracting the negative is the same as adding the positive; definition of subtraction
-3 + 4/3 = <-- multiplies the fractions first per order of mixed operations
-9/3 + 4/3 <-- common denominator is 3
= -5/3
So the equation of the perpendicular line is y = -1/3X + -5/3 = -1/3X-5/3
Notice when X=4, y = -1/3(4) - 5/3 = -4/3 - 5/3 = -9/3 = -3 as expected