Can u tell me where to plot the points and the original slope and the perpendicular slope

 The parallel line will have the same slope as the original line.

The slope of the original line is 1.   0-(-6)/6-0 is 6/6.

Try (0,-3) and (3,0)  or (-6,0) and (0,6) for a parallel line.

The perpendicular line will be the reciprocal and will have the opposite sign,

In this example, the slope is 1. 1 is the reciprocal of itself. The opposite sign makes the slope of the perpendicular line -1

Step-by-step explanation: The slope is rise/run.

Get the coordinates by going from left to right. Farthest Left is the First Coordinate.

 The rise is the Difference in y-values: take the y of the second coorodinate, y₂ and subtract the y-value of the first coordinate, y₁ This is the numerator, the top of the fraction.

The denominator is the run, the difference in x-values.  Take the x-value of the second coordinate x₂ and subtract the x-value of the first coordinate.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

step-by-step explanation: