The equation provided is $y = 25x + 200$, where $y$ represents the total earnings (in dollars) when Brian sells $x$ cameras.

Step 1: Determine the rate of change (slope).

The rate of change in a linear equation is the coefficient of $x$, which is $25$ in this case. This represents the amount Brian earns per camera sold.

Step 2: Determine the initial value (y-intercept).

The initial value is the constant term in the equation, $200$. This represents Brian's base earnings, likely a fixed amount (e.g., a salary or a starting bonus).

Interpretation:

• Rate of Change: Brian earns $25 for each camera sold. This could be a commission for each camera.
• Initial Value: Brian starts with $200, which could represent his base pay or an amount he earns regardless of selling cameras.

Do you want further clarification or detailed examples? Let me know!

Here are 5 related questions to deepen your understanding:

1. What does the total earnings $y$ become if Brian sells 10 cameras?
2. How many cameras does Brian need to sell to double his initial amount ($400)?
3. What happens to the equation if the commission rate increases to $30 per camera?
4. Can you graph the equation and describe what the slope and intercept mean visually?
5. How would the equation change if Brian received a higher base pay of $250?

Tip: To interpret linear equations, always focus on the slope (rate of change) and intercept (initial value) first—they are key!