Hudson is already 40 miles away from home on his drive back to college. He is driving 65 mi/hr. Write an equation that models the total distance d travelled after hours h. What is the graph of the equation.
When Phil started his new job, he owed the company $65 for his uniforms. He is earning $13 per hour. The cost of his uniforms is withheld from his earnings. Write an equation the models the total money he has m after h hours of work. What' is the graph of the equation?
I have no idea where to start on either of these! Please just give me an idea
1.
d = 65h
2.
m = 13h - 65
For the first scenario with Hudson driving back to college, we can use the equation:
d = 65h + 40
where:
d represents the total distance traveled in miles
h represents the hours of driving
In this equation, 65 represents the speed of the car in miles per hour, and 40 represents the initial distance of 40 miles away from home.
To visualize the graph of the equation, you can plot it on a coordinate system. The x-axis represents the hours of driving (h) and the y-axis represents the total distance traveled (d). Plot some points on the graph and connect them to get a straight line. This equation represents a positive slope, indicating that the distance traveled increases with time.
For the second scenario with Phil's job earnings, the equation can be written as:
m = 13h - 65
where:
m represents the total money earned after h hours of work
In this equation, 13 represents Phil's hourly wage, and 65 represents the initial debt of $65 for his uniforms.
Similar to the previous scenario, you can plot this equation on a coordinate system. The x-axis represents the hours of work (h), and the y-axis represents the total money earned (m). Plot some points on the graph and connect them to get a straight line. This equation represents a positive slope, indicating that the money earned increases with the number of hours worked.
For the first problem, to write an equation that models the total distance traveled after hours h, we can use the formula:
d = dh + d0
where d is the total distance traveled, dh is the distance traveled per hour, and d0 is the initial distance (in this case, 40 miles).
Given that Hudson is driving at a speed of 65 mi/hr, the equation can be written as:
d = 65h + 40
This equation shows that the total distance traveled (d) is equal to 65 times the number of hours driven (h) plus the initial distance of 40 miles.
To graph this equation, you can use a coordinate plane, where the horizontal axis represents time in hours (h) and the vertical axis represents distance in miles (d). Plot a point at (0, 40) to represent the initial distance. Then, use the slope (65) to find other points on the line. For example, after 1 hour of driving (h = 1), the distance would be 65 + 40 = 105 miles. Plot this point at (1, 105) and continue this process to plot more points. Connect the points to draw a straight line, which represents the graph of the equation.
Now, let's move on to the second problem.
For Phil's situation, to write an equation that models the total money he has after h hours of work, we can use the formula:
m = mh - c
where m is the total money earned, mh is the money earned per hour, and c is the cost of the uniforms.
Given that Phil earns $13 per hour and owes $65 for his uniforms, the equation can be written as:
m = 13h - 65
This equation shows that the total money he has (m) is equal to the amount earned per hour (13) times the number of hours worked (h), minus the cost of the uniforms (65).
To graph this equation, you can use a coordinate plane, where the horizontal axis represents time in hours (h) and the vertical axis represents the amount of money (m). Plot a point at (0, -65) to represent the initial debt. Then, use the slope (13) to find other points on the line. For example, after 1 hour of work (h = 1), the amount of money he has would be 13 - 65 = -52 dollars (which means he still owes the company $52). Plot this point at (1, -52) and continue this process to plot more points. Connect the points to draw a straight line, which represents the graph of the equation.