a car enters 15 miles north of a city. it travels due north at an average speed of 62.5 miles per hour. write an equation to model the car's distance D from the city after traveling for H hours. graph the equation
d=62.5*t+15 North
opps, change t above to H
To write an equation to model the car's distance from the city after traveling for H hours, we need to consider that the car starts 15 miles north of the city and travels at an average speed of 62.5 miles per hour due north.
The equation for the car's distance from the city after traveling for H hours can be written as:
D = 15 + 62.5H
In this equation, D represents the distance from the city, H represents the number of hours the car has traveled, and 15 represents the initial distance of the car from the city.
Now, let's graph the equation:
To create a graph, plot the hours traveled (H) on the x-axis and the distance from the city (D) on the y-axis.
Start by choosing a suitable scale for your axes, based on the range of values for H and D.
Since the car starts at 15 miles north of the city, we can set the y-axis range to start from 0 to provide a clear visualization.
For the x-axis, determine a suitable range of values for H based on the desired duration of the trip or the timeframe you want to display.
Once the axes are set up, plot points on the graph by substituting various values of H into the equation D = 15 + 62.5H and calculating the corresponding D values.
For example:
- If H = 0, D = 15 + 62.5(0) = 15 miles
- If H = 1, D = 15 + 62.5(1) = 77.5 miles
- If H = 2, D = 15 + 62.5(2) = 140 miles
Plot these points on the graph and connect them with a straight line.
The resulting graph should show a diagonal line with a positive slope, indicating that the car's distance from the city increases linearly with time.
Please note that the graph can be interactive in graphing software or drawn on a graph paper for a more accurate representation.