Wild Water Adventure Waterslides park charges a rental fee plus $2 per hour to rent inflatable rafts. The total cost to rent a raft for 4 hours is $12.50. Assume the relationship is linear. Find the rate of change and the initial value. Then move on to part 'b' to interpret each of them.​

m = 2, initial value = 4.5 or $4.50

Step-by-step explanation:

We know that renting a raft costs 2 dollars/hr plus some rental fee that we need to find.

We also know that renting a raft for 4 hours will cost $12.50. So we can do this:

$12.50 - (2.00 × 4 hrs) = $4.50, which is the "b" in the standard equation for y = mx + b

So, our equation is y = 2x + 4.5

The rate of change is the slope, which is the coefficient of the x.

m = 2

Our initial value is when x = 0.

y = 2(0) + 4.5

y = 4.5

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer