Question 835788
How if you try a data table for different values of x?


x__________y
0__________C
1_________D+C
2________2D+C
3________3D+C


The meaning of slope is, vertical change divided by horizontal change.
Slope from x of 0 to 1 is {{{(D+C-C)/(1-0)=(D+0)/1=D}}}.
If you find the slope for all of the successive points of the table, you WILL FIND:


x__________y_______slope
0__________C
1_________D+C______D
2________2D+C______D
3________3D+C______D


Students at the introductory and intermediate algebra levels are plainly told, that the product of slopes of perpendicular lines in a plane is {{{-1}}}.
This means for your example form equation of the line y=Dx+C, that the slope of the line perpendicular must be  {{{m*D=-1}}}, giving {{{highlight(m=-(1/D))}}}.