Could someone please answer these questions for me. It is for a grade and due on Tuesday, 4/24/07. The license fee for a car varies directly with the value of the car. The fee for a car that is valued at $19,500 is $292.50. a) What is the constant of proportionality? b) Write the equation that shows the license fee as a function of the value of the car. c) If you were to draw the graph of this function, what would be the slope of the line? d) If you were to draw the graph of this function, what would be the y-intercept? e) At this rate, what is the license fee for a car that is valued at $25,400?
I will be happy to critique your work on this.
Thank you, I am working on it now. Will post answer soon. Merl
14.
To answer these questions, we need to understand the concept of direct variation and how it applies to this scenario. Direct variation means that two quantities vary in proportion to each other. In this case, the license fee for a car varies directly with the value of the car.
a) The constant of proportionality is a value that tells us how the two quantities are related. To find the constant of proportionality, we can use the given information that the fee for a car valued at $19,500 is $292.50.
We can set up the equation: fee = constant of proportionality * value
Plugging in the given values, we have: 292.50 = constant of proportionality * 19,500
To find the constant of proportionality, we can divide both sides of the equation by 19,500:
constant of proportionality = 292.50 / 19,500
Simplifying this, we find that the constant of proportionality is 0.015.
b) Now, we can write the equation that shows the license fee as a function of the value of the car using the constant of proportionality we found. Let's call the license fee "L" and the value of the car "V". The equation is:
L = 0.015V
c) If we were to draw the graph of this function, the slope of the line would represent the rate at which the license fee changes with respect to the value of the car. In this case, the slope of the line would be equal to the constant of proportionality, which we found to be 0.015.
d) The y-intercept represents the point where the graph intersects the y-axis. In this case, the y-intercept would be the license fee when the value of the car is zero. Since the value of a car cannot be zero, the y-intercept is not applicable in this context.
e) To find the license fee for a car valued at $25,400, we can plug this value into the equation we found in part b:
L = 0.015 * 25,400
Evaluating this expression, we find that the license fee for a car valued at $25,400 is $381.
In summary:
a) The constant of proportionality is 0.015.
b) The equation that shows the license fee as a function of the value of the car is L = 0.015V.
c) The slope of the line representing the graph of this function is 0.015.
d) The y-intercept is not applicable in this context.
e) The license fee for a car valued at $25,400 is $381.