1. **State the problem:** You and your friend run at different constant speeds. After 1 minute, your friend is 45 meters ahead. After 3 minutes, your friend is 105 meters ahead. We need to find the equation for the distance $y$ your friend is ahead after $x$ minutes. 2. **Identify the variables:** Let $x$ be the time in minutes. Let $y$ be the distance your friend is ahead in meters. 3. **Use the slope-intercept form:** The equation of a line is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 4. **Calculate the slope $m$:** Slope $m = \frac{\text{change in } y}{\text{change in } x} = \frac{105 - 45}{3 - 1} = \frac{60}{2} = 30$ 5. **Find the y-intercept $b$:** Use the point $(1, 45)$: $$45 = 30 \times 1 + b$$ $$b = 45 - 30 = 15$$ 6. **Write the equation:** $$y = 30x + 15$$ 7. **Interpretation:** The distance your friend is ahead increases by 30 meters every minute, starting 15 meters ahead at time zero.