Day 10 Slope Applications

​Interpreting Slope Applications

By Darryl Padgett

Fill in the Blank

Can you find the mistake?

Enter your answer

Multiple Choice

Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint:  Write your formula and then simplify it.)

• a_n = 2 + 6n

• a_n = -6 + 6n

• a_n = 6n - 4

• a_n = 4 - 6n

Multiple Choice

Find the 35th term in the arithmetic sequence: -10, -14, -18, -22, ...

• -216
• -148
• -146
• -150

Multiple Choice

A.2A: Which graph best represents a function with a domain of all real numbers less than or equal to 6?

Multiple Choice

What is the Domain or the graph in Set builder Notation?

• {x| 0 ≤ x < 3}

• 0 < y ≤ 3

• {y| -2 ≤ y < 1}

• 0 ≤ x < 3

Multiple Choice

Write the following solution in interval notation:

x ≥ -3

• [ -3, ∞ )

• ( -3, ∞ )

• ( -∞ , -3 )

• ( -∞ , -3]

Multiple Select

Which function(s) represents a non-linear function.

Select all that apply.

Multiple Choice

Express [4,-10) in set builder notation.

• $$\left\{x|-10<x\le4\right\}$$

• $$\left\{x\ |\ 4<x<-10\right\}$$

• {x | -10 < x < 4}
• {x | x > 4}

Multiple Choice

Express the following in Interval Notation.

$$\left\{x|-10\le x<5\right\}$$

• (-10, 5)
• [-10, 5]
• [-10, 5)
• (-10, 5]

Multiple Choice

Identify the domain and range of the function.

• Domain: -6 ≤ x ≤ 2

  Range: -3 ≤ y ≤ 5

• Domain: All real number

  Range: -3 ≤ y ≤ 5

• Domain: All real numbers

  Range: y ≤ 3

• Domain: All real numbers

  Range: $$y\ge-3$$

Multiple Choice

If f(x) = 19, Find the value for x.

• x = 0

• x = 1

• x = 2

• x = 3

Multiple Choice

Write an equation of the line where the

Slope = -3, y-intercept = 2

• y = 2x - 3

• y = -3x + 2

• y = 3x - 2

• y = 2x + 3

Multiple Choice

Which equation matches the table?

• y = 3x + 9
• y = x + 9 
• y = x + 3
• y = 12x - 3

Multiple Choice

What is f(6) for the function f(x)=3x-8

• -8

• 10

• -144

• answer not here

Slope from a graph

Positive: going up the hill, incline

Negative: going down the hill, decline

Undefined: vertical line (up and down)

Zero: horizontal line (side to side)

Use these key words to answer the following questions

Identifying Slope in a Word Problem

• The slope in a word problem is the rate of change.

• As it is a rate, you will often see the slope associated with words like "each" or "per" (ex: she paid x dollars for each item, he charged x dollars per hour).

• The y-intercept in a word problem is the starting point or initial value.

Let x = 12 and substitute it into the equation above.
y = 1.5(12) + 4 = 22
It will cost $22 to rent the bike for 12 hours.

Writing Linear Equations

• Mr. Gill joined a gym to work off his Thanksgiving calories. The starting cost for joining the gym was $100. It costs $20 per month to stay in the gym. Write an equation to model the total cost per month.

• y = mx + b

• Total Cost = ($20)(# of months) + $100

• C = 20m + 100

Multiple Choice

A dude ranch in Texas charges customer y dollars to go horseback riding based on the equation y = 10x + 20, where x represents the hours they go horseback riding. What is the meaning of the slope?

• The initial fee for riding horses is $10

• It cost $10 per hour to ride a horse

• The initial fee for riding horses is $20

• The total cost for riding horses is $20

Multiple Choice

In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. Write an equation in slope-intercept form that models this situation.

• y = 30x + 4

• y = 4x - 30

• y = -4x + 30

• y= 4x + 30

Multiple Choice

In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation in slope-intercept form that models this situation.

• y=5x+20

• y= -5x + 20

• y = 20x + 5

• y = 20x + 5x

Multiple Choice

Chance is saving money to buy the new Jordans. He started with $25 and is saving $15 per week. Write an equation that models this situation.

• y= -25x + 15

• y= 25x + 15

• y= -15x + 25

• y=15x + 25

Fill in the Blank

Harry Potter has 10,000 gold coins in his vault at Gringotts. Each week, he takes outs 850 gold coins for his expenses. Function g gives the remaining amount of gold coins as a function of the number of weeks, w, since Harry started taking out the gold coins.

How many gold coins did Harry have remaining after two weeks?

Multiple Choice

Basmala is saving money to buy new iphone. She has saved $50 so far and plans to $20 each week for the next few months. Write an equation that represents how much money she will have after x weeks.

• y = 50x + 20

• y = -50x + 20

• y = 20x + 50

• y = -20x + 50

Multiple Choice

A dude ranch in Texas charges customer y dollars to go horseback riding based on the equation y = 10x + 20, where x represents the hours they go horseback riding. What is the meaning of the y-intercept?

• The initial fee for riding horses is $10

• It cost $10 per hour to ride a horse

• The initial fee is for riding horses is $20

• It cost $10 per hour to ride a horse

Multiple Choice

Raegan is driving down a mountain. Her elevation, y (in feet), is represents by the equation y = -35x + 5450, where x is the minutes since she started driving. What is the meaning of the y-intercept?

• Raegan started her trip down the mountain at 5,450 feet

• Raegan started her trip down the mountain at 35 below feet sea level

• Raegan is driving down the mountain at 5,540 feet per minute

• Raegan is driving down the mountain at 35 feet per minute

Multiple Choice

A science class collected data measuring the amount of water in a bucket that was out in the Sun. The equation w = -1.5h + 18 represents how much water, w , was in the bucket after hours, h. According to this equation, how many hours did it take for the bucket to be emptied? Hint: let w = 0 and solve for x.

• 6

• 10

• 12

• 18

Multiple Choice

The height in inches of concrete being poured for a foundation can be found using the function y = 15 + 2.5x, where x is the number of minutes. If the concrete is poured between 5 and 10 minutes, find the domain and range of this situation.

• Domain: $$5\le x\le10$$ Range: $$27.5\le y\le40$$

• Domain: $$27.5\le x\le40$$ Range: $$5\le y\le10$$

• Domain: {5, 6, 7, 8, 9, 10} Range: {28, 29, 30, ..., 40}

• Domain: {28, 29, 30, ..., 40} Range: {5, 6, 7, 8, 9, 10}

Multiple Choice

The daily cost of hiring a plumber, y, to work x hours on a repair project can be modeled using a linear function. The plumber charges a fixed cost of $80 plus an additional cost of $45 per hour. The plumber works a maximum of 8 hours per day.

For one day of work, what is the range of the function for this situation?

•  $$0\le x\le8$$

• $$80\le y\le440$$

• $$0\le x\le10$$

• $$45\le y\le685$$

Multiple Choice

Mae worked at a summer camp where she earned $20 plus $7 an hour each week. The amount of money she earned each week, e, is a function of the number of hours she works, h. Mae could not work more than 20 hours each week.

What is the domain/range? Note: Mae can work part of an hour.

• Domain: {0, 1, 2, 3, ..., 20}

  Range: {20, 27, ..., 160}

• Domain: {20, 27, ..., 160}

  Range: {0, 1, 2, 3, ..., 20}

• Domain: $$0\le x\le20$$

  Range: $$20\le y\le160$$

• Domain: $$20\le x\le160$$ Range: $$0\le y\le20$$