The manager of a local hotel knows that on holiday weekends if they charge $112 per room, they will book all 100 of the rooms in the hotel. For every $40 increase in price, they will book 5 fewer rooms. In the following parts we will write an equation that represents the number of rooms rented as a function of price charged per room. Part a)

Identify the input and output to the function and the variables that you will use to represent them.

Part b)

Using the input and output from Part a) create a table that includes at least 5 different room charges and the corresponding number of rooms that are rented.

Part c)

Based on the table you created in Part b) what type of function does this table represent? How do you know?

Part d)

Using the above parts, write an equation that represents the number of rooms rented as a function of price charged per room. (Make sure to show all work)

Write the equation of a line that is perpendicular to the given line and that passes through the given point. –3x – 6y = 17; (6, 3) y = x – 9 y = 2x – 9 y = –2x – 9 y = x + 0 3. is the relationship shown by the data linear? if so, model the data with an equation. x y 1 5 5 10 9 15 13 20 the relationship is linear; y – 5 = (x – 1). the relationship is not linear. the relationship is linear; y – 5 = (x – 1). the relationship is linear; y – 1 = (x – 5). write an equation in point-slope form for the line through the given point with the given slope. (–10, –1); m = y + 10 = (x + 1) y – 1 = (x – 10) y – 1 = (x + 10) y + 1 = (x + 10) 5. write an equation for each translation of . 6.5 units up y + 6.5 = | x | y = | 6.5 x | y = | x | + 6.5 y = | x | – 6.5 6. write an equation for each translation of . 5.5 units right y = | x | + 5.5 y = | x – 5.5 | y = | x | – 5.5 y = | x + 5.5 | 7. which equation translates y = | x | by 8 units to the left? y = | x | – 8 y = | x | + 8 y = | x – 8| y = | x + 8|