Question

The linear model represents the height of a water balloon thrown off the a building over time, measured in seconds. Part a: During what intervals of the domain is the water balloon's height increasing? Part b: During what intervals of the domain is the water balloon's height staying the same? Part c: During what intervals of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. Part d: Use the constraints of the real-world situation to predict the height of the water balloon at 14 seconds. Use complete sentences to support your answer.

Answer 1

The water balloon's height increases when the slope of the linear model is positive, stays the same when the slope is zero, and decreases the fastest when the slope is negative and has a larger absolute value. To predict the height at 14 seconds, substitute x = 14 into the linear model equation.

Step-by-step explanation:

Part a: The water balloon's height is increasing during intervals where the slope of the linear model is positive. In other words, when the line on the graph is going upwards. For example, if the balloon's height is represented by the equation y = mx + b, where y is the height and x is the time in seconds, then the water balloon's height is increasing when the value of m is positive.

Part b: The water balloon's height stays the same during intervals where the slope of the linear model is zero. In other words, when the line on the graph is horizontal. For example, if the balloon's height is represented by the equation y = mx + b, where y is the height and x is the time in seconds, then the water balloon's height stays the same when the value of m is zero.

Part c: The water balloon's height is decreasing the fastest during intervals where the slope of the linear model is negative and the magnitude of the slope is highest. In other words, when the line on the graph is going downwards with a steeper slope. For example, if the balloon's height is represented by the equation y = mx + b, where y is the height and x is the time in seconds, then the water balloon's height is decreasing the fastest when the value of m is negative and has a larger absolute value.

Part d: To predict the height of the water balloon at 14 seconds, we need the equation of the linear model. Assuming the equation is y = mx + b, where y is the height and x is the time in seconds, we can substitute x = 14 into the equation and calculate the value of y to find the height of the water balloon at 14 seconds.