Each week Maya buys 9 new stickers. In a linear equation, which part shows how much $y$ changes when $x$ increases by 1?

Recall that a linear equation can be written as $y = mx + b$, where $m$ is the change per week and $b$ is the starting amount. Match these to the numbers in the story.

Try plugging in $x = 1$ (after 1 week) into each equation. Which one gives a total equal to the starting number of stickers plus 9?

Type each option into Desmos as separate functions, for example: y = 35x + 9, y = 9x + 35, y = 44x, and y = 35x - 9 so you can compare them on the same graph.

Use a table for each function (tap the gear icon, then "Table") or tap on the point where $x = 0$. Identify which equation(s) give $y = 35$ at $x = 0$, since Maya starts with 35 stickers before any weeks pass.

Now compare the values from $x = 0$ to $x = 1$ in the table. The correct equation will increase $y$ by 9 from week 0 to week 1, matching the story that she buys 9 stickers each week. The equation that has both the correct starting value and this weekly increase is the one that represents the situation.

The problem says $x$ is the number of weeks after Maya began buying stickers, and $y$ is the total number of stickers she has. So:

• When $x$ increases by 1, one week has passed.
• $y$ is how many stickers she has at that time.

Maya already had 35 stickers in her collection before she started buying new ones each week. That means at $x = 0$ weeks, $y = 35$ stickers. In a linear equation of the form $y = mx + b$, this starting value is $b$ (the y-intercept). So here, $b$ must be 35.

She buys 9 new stickers each week. That means every time $x$ increases by 1 (one more week), $y$ increases by 9 stickers. In the equation $y = mx + b$, the number you multiply by $x$ (the coefficient of $x$) is the slope $m$, which represents the change per week. So here, $m$ must be 9.

Use the slope-intercept form $y = mx + b$ with $m = 9$ and $b = 35$ to get the model:

Quick check:

• At $x = 0$: $y = 9(0) + 35 = 35$ stickers (the starting amount).
• After 1 week ($x = 1$): $y = 9(1) + 35 = 44$ stickers (35 plus 9 more). This matches the situation, so $y = 9x + 35$ is the correct equation.