Day 10 Slope Applications

​Interpreting Slope Applications

By Darryl Padgett

Fill in the Blanks

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 Blanks

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: $$0\le y\le20$$