Interval and slope of a line
SŠ10 minGrading a line, its trace point and the relation i · s = 1.
Graded points
The height IS the third dimension. It is not drawn – it is written beside the point.
The line AB
- Plan length d
- 6.04
- Rise Δh
- 3.00
- Interval i
- 2.01
- Slope s
- 0.50
- Slope in %
- 49.7%
- Slope angle
- 26.41°
- True length
- 6.75
Interval and slope are reciprocals. A bigger interval means a GENTLER line, not a steeper one.
The plane ABC
- Plane interval
- 1.79
- Slope
- 0.56
- Slope angle
- 29.14°
A plane’s contours are parallel and evenly spaced – their spacing IS the plane’s interval. Raise one point’s height and watch them close up.
Show
Spatial view
Theory
A line is given by two graded points. The distance d between their views is the plan length – not the true length of the segment. The difference of the heights Δh is the rise.
The interval i = d / |Δh| is the horizontal distance per one unit of height. The slope s = |Δh| / d is the same thing seen the other way round. They are reciprocals, so i · s = 1 – and this is the source of the commonest mistake: a bigger interval means a GENTLER line, not a steeper one.
To grade a line means marking the points on it with whole-number heights. Because a line rises uniformly, those points sit exactly one interval apart – so you measure one interval and step it off. The point with height 0 is the trace point, where the line meets π₁.
Step-by-step construction
Practice
Build the construction yourself
What is the next step?
1 / 5Choose the step that comes next. The drawing only advances on a correct choice.
Check your understanding
A line has plan length 6 and a rise of 2. What is its interval?
Line a has interval 2, line b has interval 5. Which is steeper?
What is the trace point of a line in elevation projection?
Downloadable material
A PDF for this lesson is in preparation.
Need help?
Book a lesson and we will go through it together, step by step.