Question

Compare the costs of bike trips from the two companies shown. For both, the cost is a linear function of the number of days.

Answer 1

I did this quiz its Scenic Pathways has no sign up fee and a greater cost per day.

Answer 2

Answer:

Scenic Pathways has no sign up fee and a higher cost per day.

Step-by-step explanation:

Let y represent the total cost for Backcountry Tours.  Let x represent the number of days.

Since they charge $35 per day, this gives us the expression 35x.  We add to this the $25 sign up fee; this gives us 35x+25.  Together this is the total, which gives us the equation

y = 35x+25

For Scenic Pathways, we first find the slope.  We will use the first two points:

$m=\frac{y_2-y_1}{x_2-x_1}\\\\=\frac{90-45}{2-1}=\frac{45}{1}=45$

Then using this slope and the first point, we use point-slope form:

$y-y_1=m(x-x_1)\\\\y-45=45(x-1)$

We will rewrite this into slope-intercept form:

y-45 = 45(x-1)

Use the distributive property on the right hand side:

y-45 = 45(x)-45(1)

y-45 = 45x-45

Add 45 to each side:

y-45+45 = 45x-45+45

y = 45x

This means the cost per day, where x is the number of days, is $45.  Since there is nothing added to this, there is no sign up fee.