1. **State the problem:** We have a tile pattern starting with 5 tiles in Figure 0 and adding 7 tiles for each new figure. We want to find the equation representing the number of tiles $y$ in figure number $x$. 2. **Understand the pattern:** The initial number of tiles (when $x=0$) is 5. Each time $x$ increases by 1, 7 tiles are added. 3. **Write the general formula for linear growth:** $$y = mx + b$$ where $m$ is the rate of change (tiles added per figure) and $b$ is the initial amount (tiles at figure 0). 4. **Identify $m$ and $b$:** - $m = 7$ (tiles added each figure) - $b = 5$ (initial tiles) 5. **Write the equation:** $$y = 7x + 5$$ 6. **Check the options:** - $y = 5x + 7$ (incorrect, initial value and rate swapped) - $2y + 14x = 10$ (does not match the pattern) - $-10x + 7y = 3$ (does not match the pattern) - $y = 7x + 5$ (correct) **Final answer:** $$y = 7x + 5$$