1. The problem gives two equations: $y=3m+4$ and $x=5m-6$. 2. These equations express $y$ and $x$ in terms of the parameter $m$. 3. To understand the relationship between $x$ and $y$, we can eliminate $m$. 4. From $x=5m-6$, solve for $m$: $$m=\frac{x+6}{5}$$ 5. Substitute this into $y=3m+4$: $$y=3\left(\frac{x+6}{5}\right)+4=\frac{3(x+6)}{5}+4=\frac{3x+18}{5}+4=\frac{3x+18}{5}+\frac{20}{5}=\frac{3x+38}{5}$$ 6. So the relationship between $x$ and $y$ is $$y=\frac{3x+38}{5}$$ 7. This is a linear equation in $x$ and $y$. Final answer: $$y=\frac{3x+38}{5}$$