A car enters an interstate highway 15 mi north of a city.The car travels due
north at an average speed of 62.5 mi/h.Write an equation to model the car’s
distance d from the city after traveling for h hours. Graph the equation
The equation to model the car's distance, d, from the city after traveling for h hours can be calculated using the formula:
d = 15 + 62.5h
In this equation, 15 represents the initial distance of the car from the city (15 mi north of the city), and 62.5h represents the distance traveled by the car in h hours at an average speed of 62.5 mi/h.
Graphing this equation would result in a straight line with a positive slope of 62.5. The y-intercept of the graph would be 15, indicating the initial distance from the city. The x-axis represents the time in hours, and the y-axis represents the distance from the city in miles.
To write an equation that models the car's distance from the city after traveling for h hours, we need to consider that the car travels due north at an average speed of 62.5 mi/h. Since the car is always traveling north, the distance it covers can be represented by a linear equation.
Let's assume the car's initial distance from the city is 0 miles. As the car travels due north, its distance from the city will increase by 62.5 miles for every hour it travels.
Therefore, the equation that models the car's distance from the city after h hours can be written as:
d = 62.5h
where d is the distance from the city and h is the number of hours the car has traveled.
To graph this equation, plot the values on a graph with the distance (d) on the y-axis and the time (h) on the x-axis. Start with the car's initial distance of 0 miles (h = 0) and then plot additional points by substituting different values of h into the equation to find the corresponding values of d.
For example, when h = 1:
d = 62.5 * 1 = 62.5
So, the car's distance from the city after 1 hour is 62.5 miles. Plot this point on the graph.
Continue to find more points by substituting other values for h, such as h = 2, h = 3, and so on. Plot these points on the graph and then connect them to form a straight line. This line represents the car's distance from the city as it travels north at a constant speed of 62.5 mi/h.