The graph shows distance in feet as a function of time in seconds. Write an equation for the function and describe a situation that it could represent. Include the initial value and rate of change for the function and what each of these values represents in this situation.

To create an equation for a function that represents distance as a function of time, we can use the linear equation format: \[ d(t) = mt + b \] where: - \(d(t)\) is the distance in feet, - \(m\) is the rate of change (slope) in feet per second, - \(t\) is the time in seconds, - \(b\) is the initial value (y-intercept), which represents the initial distance at \(t = 0\). ### Step 1: Identify the Initial Value and Rate of Change 1. **Initial Value (\(b\))**: This is the distance at \(t = 0\). For example, if the graph shows that the distance is 10 feet when \(t = 0\), then \(b = 10\). 2. **Rate of Change (\(m\))**: This is the slope of the line, representing how much distance changes per unit of time. For instance, if the graph indicates that the distance increases by 5 feet every second, then \(m = 5\). ### Step 2: Write the Equation Using the values identified: - If \(b = 10\) (initial distance) and \(m = 5\) (rate of change), the equation would be: \[ d(t) = 5t + 10 \] ### Step 3: Describe a Situation This equation could represent a scenario where a person is walking away from a starting point. For example, imagine a person starts walking from a point 10 feet away from a reference point (like a starting line) and walks at a constant speed of 5 feet per second. ### Summary of Values - **Initial Value (\(b\))**: 10 feet - This represents the starting distance from the reference point. - **Rate of Change (\(m\))**: 5 feet/second - This indicates the speed at which the person is walking away from the starting point. In conclusion, the function \(d(t) = 5t + 10\) describes the distance of a person walking away from a starting point at a constant speed, starting from 10 feet away.