Show questions Your total cost C to skate at Skate Days is a $2 skate rental plus an additional $3.25 for each hour Chat
you skate.
Write a function rule to represent the situation.
19
Is this situation continuous or discrete? Explain your reasoning.
Create a sign that Skate Days can display at the counter that tells people how much it will cost
for each hour they skate (include 1-5 hours on your sign)
Skate City has free skate rental but charges $4 for each hour.
Which skating rink would you choose to go to?
Why did you make that choice? Use mathematical reasoning to support your answer. Lo

The cost is a fixed $2, plus $3.25 for any additional hour.

Then if you rent it for x hours, the cost is:

c(x) = $2 + $3.25*x

Is this situation continuous or discrete?

Yes, it is discrete, because x is "the number of hours"

so if you rent it for 1.30 hours, they will say "ok, this is equivalent to two hours".

This means that while the values of x are continuous, the possible costs are:

{$2, $2 + $3.25, $2 + 2*$3.25, }

Which is a discrete set.

Then the sign for 1 to 5 hours will be:

1 hour $2 + $3.25 = $5.25

2 hours $2 + 2*$3.25 = $8.50

3 hours $2 + 3*$3.25 = $11.75

4 hours $2 + 4*$3.25 =  $15

5 hours $2 + 5*$3.25 = $18.25

In the other park the cost is only $4 for each hour (no fixed cost) then the total cost for x hours is:

c(x) = $4*x

Now, which option is better?

If we look at the costs for different numbers of hours for this other equation, we have:

1 hour $4

2 hours 2*$4 = $8

3 hours 3*$4 = $12

4 hours 4*$4 = $16

Then: if you want to skate 2 hours or less, Skate City is cheaper, if you want to skate more than that, kate Days is cheaper.

This happens because the first one has a smaller slope, meaning that is larger at first, but as x grows the price does not grow as much as in Skate City

y=mx+b

step-by-step explanation:

m slope

b y-intercept

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form