simple linear relationships

there is an argument for working with (linear) relationships before equations
because the variables properly vary rather than being 'as-yet-unknown' numbers - that can be found
such work could precede straight line graphs
maybe lending further insight into the gradient (equal steps)

I'm told that in Hungary the maths curriculum starts from this more general appreciation before moving to the simpler, equation, cases (Paul Andrews' various articles with Gillian Hatch when he was at Manchester Metropolitan, Cambridge, now at Stockholm e.g. for BSRLM) 

when one of the variables is fixed you then have a linear equation

the intention of these tasks is that students find integer pairs that fit the rules, positive integers initially

they may well notice patterns that enable other pairs to be more easily found and lead this work into negative numbers

the Cuisenaire rod resources 'rod relationships' might be one way to begin such an exploration