i-Ready Linear Functions: Model from a Verbal Description - Quiz - Level H Rebecca is flying a drone at a constant height. She decides to make the drone rise vertically. It rises 18 m every 3 s . After 5 s , the drone is at a height of 40 m . The drone's height in meters, \( y \), is a function of the time in seconds, \( x \). How many meters does the drone rise each second? Find the rate of change. 6 meters per second What is the height of the drone before Rebecca makes it rise? Find the initial value. 10 meters Write an equation to represent the function. \[ y=\square x+? \] 7 B 9 E

Let's break down the problem step by step. ### Step 1: Determine the rate of change Rebecca's drone rises 18 meters every 3 seconds. To find the rate of change (the rise per second), we can use the formula: \[ \text{Rate of change} = \frac{\text{Rise}}{\text{Time}} = \frac{18 \text{ m}}{3 \text{ s}} = 6 \text{ m/s} \] So, the drone rises **6 meters per second**. ### Step 2: Find the initial value After 5 seconds, the drone is at a height of 40 meters. Since the drone rises at a rate of 6 meters per second, we can calculate how much it has risen in those 5 seconds: \[ \text{Height after 5 seconds} = \text{Initial height} + \text{Rate of change} \times \text{Time} \] Let \( h \) be the initial height. Then we have: \[ 40 \text{ m} = h + 6 \text{ m/s} \times 5 \text{ s} \] Calculating the rise in height: \[ 6 \text{ m/s} \times 5 \text{ s} = 30 \text{ m} \] Now substituting back into the equation: \[ 40 \text{ m} = h + 30 \text{ m} \] Solving for \( h \): \[ h = 40 \text{ m} - 30 \text{ m} = 10 \text{ m} \] So, the initial height of the drone before Rebecca makes it rise is **10 meters**. ### Step 3: Write the equation The height \( y \) of the drone as a function of time \( x \) can be expressed in the form: \[ y = mx + b \] Where: - \( m \) is the rate of change (slope), which we found to be 6. - \( b \) is the initial height, which we found to be 10. Thus, the equation representing the function is: \[ y = 6x + 10 \] ### Final Answer 1. The drone rises **6 meters per second**. 2. The initial height is **10 meters**. 3. The equation representing the function is: \[ y = 6x + 10 \]