1. The problem states the relationship between the family donation $x$ and the matching contribution $y$ from local businesses is given by the equation $y = 0.6x$. 2. This is a direct proportionality problem where $y$ is directly proportional to $x$ with a constant of proportionality $0.6$. 3. The formula used is $y = kx$ where $k$ is the constant of proportionality. 4. To find the matching contribution $y$ for any family donation $x$, multiply $x$ by $0.6$. 5. For example, if the family donates $100$, then the matching contribution is: $$y = 0.6 \times 100 = 60$$ 6. This means local businesses will contribute $60$ when the family donates $100$. 7. This linear relationship means for every unit increase in $x$, $y$ increases by $0.6$ units. Final answer: The matching contribution $y$ is $0.6$ times the family donation $x$, or $y = 0.6x$.