Collecting metrics from an application in Graphite+Grafana?

Question

Monitoring

There is a service from which we want to build 2 graphs: the number of 500th errors and the X value returned by the rest api. I installed Graphite + Grafana on the machine, I seem to have figured out this bundle, but have not yet figured out how to work with it correctly.
The X value is apparently just sent from the service to Graphite as a metric.
But what about the number of errors? Make a counter inside the application and send it at intervals or analyze the logs (with what?)
Correct / suggest the correct path.