1. The problem states that David starts with 50 cards and adds 45 cards each month. 2. We want to write an equation for $y$, the total number of cards after $x$ months. 3. The total number of cards after $x$ months is the initial amount plus the number of cards added each month times $x$. 4. The formula is: $$y = 50 + 45x$$ 5. This is a linear equation where 50 is the starting amount (initial value) and 45 is the rate of increase per month. 6. So, the equation to find the total number of cards after $x$ months is $$y = 50 + 45x$$.