Write down the following formula -- y = mx + b. X equals the point on the horizontal (x) axis for the line and Y equals the point on the vertical (y) axis for the line. B equals the point where the line crosses the vertical axis at x=0. M will be the line's slope -- how many points vertically the line rises for each point horizontally it runs.
Draw a cross. These will be the horizontal (x) and vertical (y) axes.
Draw your diagonal line on the cross.
Measure the distance from the origin (center) of the cross to the point where the diagonal crosses the vertical (y) axis. This is your value for "b." You may use any unit you like here -- inches, centimeters or abstract "points" -- as long as you use the same units for the rest of the procedure.
Measure how far the diagonal rises or falls as it runs one unit along the horizontal (x) axis and divide your value for "m." That is your value for "m," the slope. For example, if the diagonal is at 5 at x=0 and 6 at x=1, then your slope is 1.
Write down the Pythagorean theorem -- c² = a² + b². This theorem is normally used to find the length of the longest side of a right triangle using the two other sides, but it can also be used to find the length of any diagonal line because any diagonal line can be turned into a right triangle by adding two more lines -- a vertical and horizontal line.
Measure how far the diagonal travels horizontally. This is the value for "a."
Measure how far the diagonal travels vertically. This is your value for "b."
Put your values for "a" and "b" into the formula and solve. For example, if the diagonal was 3 units long horizontally and 4 units long vertically, then:
c² = a² + b²
c² = (3)² + (4)²
c² = 9 + 16
c² = 25
c = square root (25)
c = 5
This example works out cleanly, but you may want a calculator to find the square root at the end of the problem.