Graphs are more to present data. For example, if you wanted to organize and list mountains by their heights. You would need to mentally organize your data, or put each item on an index card so you can move them around to organize the data. Then, pick the type of graph you need to use to best represent the data you have.
If you mean construct an image or a depiction, it would be like any other drawing, with or without labels.
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A protractor is normally used to construct angles.
you might not be able to construct all the angles, but using a compass you can construct some angles by constructing angular bisectors. eg:construct angular bisector of straight line i.e; 180 degrees it gives 90 degrees
When you graph a line using only the slope and a point, you start by graphing the point.
A 10 degree angle cannot be constructed using only a compass and straight edge.
No, it is not possible to construct a cube of twice teh volume of a given cube using only a straightedge and a compass.