The scale that will produce the smallest drawing would be b) 1mm:50m.
First, I converted all the measurements to centimeters:
a) 1cm:500cm
b) 0.01cm:5000cm
c) 5cm:1000cm
d) 10cm:2500cm
Then, you divide the scales:
a) 0.002
b) 0.000002
c) 0.005
d) 0.004
B is the smallest number, meaning it will be the smallest scale.
This is the concept of algebra, to get the slope of the line we need to rewrite the equation in slope intercept form y=mx+c, where m=slope, c=y-intercept.
Therefore re-writing our expression in slope-intercept form we get:
7x-3y=10
-3y=-7x+10
y=7/3x-10/3
The slope=7/3
hence we conclude that the slope of the line perpendicular to this is -3/7
ALL LINES CAN BE REPRESENTED IN THE FORM 
.
We know that:
and
Observe that:
So:
But we know that 
, so:
Since:
So the line is:
Let us assume the common ratio to be = x
Then
(1 * x) + (4 * x) = 50
x + 4x = 50
5x = 50
x = 50/5
= 10
So from the above deduction, we get the common ratio to be equal to 10
Then
The smallest number = 1 * x
= 1 * 10
= 10
