A function to show the cost in dollars (y) of hiring a car for d days is y = 15d + 35.
The table of values should be completed as shown below.
A graph of the function is shown in the image below.
The cost of hiring a car for 7 days is $140.
The fixed charge represents the y-intercept of the graph.
In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
- m represents the slope or rate of change.
- x and y are the points.
- c represents the y-intercept or initial value.
Based on the information provided about this puppy, we have the following slope and y-intercept;
Slope, m = $15 (cost per day).
y-intercept, c = $35 (fixed charge).
By substituting these parameters, an equation that models the cost of hiring a car for d days is given by;
y = mx + c
y = 15d + 35
The table of values should be completed as follows;
d function rule y ($)
0 y = 15(0) + 35 35
1 y = 15(1) + 35 50
2 y = 15(2) + 35 65
3 y = 15(3) + 35 80
4 y = 15(4) + 35 95
5 y = 15(5) + 35 110
8 y = 15(8) + 35 155
When d is 7, the cost of hire is given by;
y = 15(7) + 35
y = $140
In conclusion, we can logically deduce that the fixed charge represents the y-intercept (0, 35) of the graph.