You would have broken line graph in your case e.g.

This is also called linear spline because parts of this graph are linear (lines). Linear spline is used a lot in economics (e.g. stock prices over time). There also other types of spline: cubic, trigonometric...

On the other hand if you have some measurements e.g. distance traveled with car and fuel consumption and you suspect that relation between those two values is linear, then you would use line (not broken line) to approximate that relation. This is called linear regression. I say approximate because when you measure something you will probably make some measurement mistakes so your data points will not lie on the line, but your line needs to be close to them.

For your type of problem it's more usual to use **column chart** then broken line chart. Because those are categories (you dont have 1.5 people asigned to value 4) and line asignes values to all real numbers, while column chatr doesn't.