1. **State the problem:** We need to find the values of constants $m$ and $c$ in the linear equation $y = mx + c$ given two points: when $x=3$, $y=20$ and when $x=4$, $y=40$. 2. **Write the system of equations:** Substitute the given points into the equation: $$20 = 3m + c$$ $$40 = 4m + c$$ 3. **Solve the system:** Subtract the first equation from the second to eliminate $c$: $$40 - 20 = (4m + c) - (3m + c)$$ $$20 = 4m - 3m$$ $$20 = m$$ 4. **Find $c$:** Substitute $m=20$ back into one of the original equations, for example: $$20 = 3(20) + c$$ $$20 = 60 + c$$ $$c = 20 - 60 = -40$$ 5. **Write the final equation:** Substitute $m=20$ and $c=-40$ into $y = mx + c$: $$y = 20x - 40$$ This is the equation relating $x$ and $y$ based on the given points.