Relationship as Modeled, Not Observed

The assumption of linear regression surrounds the relationship as modeled, not the observed relationship between variables as they were initially collected. In other words, you can (sometimes) avoid violating the assumptions by transforming the independent and/or dependent variables.

For example, the scatterplot on the left shows a regression line that models age as a polynomial (aka as age + age*age)

If we model age only with age, we violate the linear assumption.

However, if we model age as a polynomial, we no longer violate the assumption. 

Interpreting polynomials can be found on the interpretation page.