What does it mean for an equation to be linear? what kind of relationships can be modeled by equations in the form y=mx?

It means an equation between two variables that gives a straight line when plotted on an graph.

HOPE THIS HELPS!

An equation that is linear:
1. When graphed, linear equations make a [straight] line (hence the name linear).
2. Have x exponents raised to the first power (in other words, if the x-value obtains exponents that are not 1 [Note: having 1 as an exponent is just like not having an exponent given that a number raised to the first power is still that number], it isn't linear) 

Proportional relationships can be modeled in the form y = mx where m equals the slope, or constant rate of change.