Answer:
The constant of variation for the subscription cost based on the number of weeks is 4
Step-by-step explanation:
The equation of a line in intercept form is given by:
y = mx + c
Where c is the intercept on the y axis and m is the slope of the line which is constant.
In this problem, we are asked to find the constant of variation, this can be determined from the slope because the slope is the constant of variation.
The Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis. The equation of a line passing through two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The points are (1, 2) and (5, 8), therefore using:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-2=\frac{8-2}{5-1}(x-1)\\ y-2=4(x-1)\\y-2=4x-4\\y=4x-4+2\\y=4x-2[/tex]
Comparing y = 4x -2 and y = mx + c, m = slope = 4
The constant of variation for the subscription cost based on the number of weeks is 4
