Functions warmup ... with a bunch of words

Jenny is a math tutor in her community.  She charges a $4 fee for gas, plus $25 per hour she tutors.  The more hours she tutors, the more money she makes.

Which of these is the independent variable in this situation? Hint: They are asking for a variable...don't provide a number as an answer...that doesn't make sense. The numbers below will be slope (m) or y-intercept (b).

• The amount of money Jenny makes.

• $25 per hour

• $4 fee for gas

• The number of hours Jenny tutors

Answer explanation

*The $4 fee for gas is the y-intercept (b)

*The $25 per hour is the slope (m)

*The Amount of money earned is our dependent variable (y)

Our x (independent variable) determines how much Bill needs to charge based on the hours worked.

Tags

CCSS.6.EE.C.9

Billy cuts grass to make extra money. He charges a $5 flat fee (one time fee to cover gas and lawn mover maintenance), plus $10 per hour it takes to cut the grass. The more hours he works, the more money he makes.

Which of these is the independent variable in this situation?

• The amount of money Billy makes.

• The $10 per hour

• The number of hours it takes to cut the grass.

• The $5 flat fee

Answer explanation

*The $5 flat fee is the y-intercept (b)

*The $10 per hour is the slope (m)

*The Amount of money earned is our dependent variable (y)

Our x (independent variable) determines how much Bill needs to charge based on the hours worked.

Tags

CCSS.6.EE.C.9

Juan and Ana are both saving money for a new phone.  Juan is saving $20 per week (m).  Ana is also saving $20 per week (m), but she started with $100 in her account (sounds like her b=100).

 Which statement best describes the difference between the graphs of these two linear relationships, where x represents the number of weeks and y represents the amount of money in their accounts?  

• The line representing Ana’s savings is steeper.

• The y-intercept of the line representing Ana’s savings
  is greater.

• The line representing Juan’s savings is steeper.

• The y-intercept of the the line representing Juan’s
  savings is greater.  

Answer explanation

The $20 PER week is the slope...the rate at which the saved money is changing. When you are saving money...you have to start with some amount...it might even be $0. Juan's b=$0 ... Ana's b=$100 ... and we know that b is the y-intercept.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Now that Juan and Ana have phones, they have to pay for data plans. Juan's plan has a $50 monthly fee plus he pays $5 per giga-byte of data used. Ana's plan also starts at $50 per month, but she pays $7 per giga-byte of data used. This time...sounds like their b's are the same, but their slopes are different (per gigabyte fee).

 Which statement best describes the difference between the graphs of these two linear relationships, where x represents the number of gigabytes used and y represents the total monthly bill?  

• The line representing Ana’s savings is steeper cause her m=$7

• The y-intercept of the line representing Ana’s total bill is greater cause his b=$50

• The line representing Juan’s savings is steeper because his m=$5

• The y-intercept of the the line representing Juan’s
  savings is greater ... cause his b=$50

Answer explanation

Remember that the larger the slope the steeper the line. m = 2 is a steeper line than m=1 for instance. (Same thing is true for negative slopes...think about the absolute value of those slopes).

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Juan and Ana are now saving saving money for a bike. Juan is saving $25 per week (m).  Ana is also saving $25 per week (m), but she started with $50 in her account (sounds like her b=50).

 Which statement best describes the difference between the graphs of these two linear relationships, where x represents the number of weeks and y represents the amount of money in their accounts?  

• The line representing Ana’s savings is steeper.

• The y-intercept of the line representing Ana’s savings
  is greater.

• The line representing Juan’s savings is steeper.

• The y-intercept of the the line representing Juan’s
  savings is greater.  

Answer explanation

The $25 PER week is the slope...the rate at which the saved money is changing. When you are saving money...you have to start with some amount...it might even be $0. Juan's b=$0 ... Ana's b=$50 ... and we know that b is the y-intercept. Poor Juan....he never has any money to start.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Which sentence is represented by the function  y= 550 - 30x?

Hey....I've been preaching y = mx + b ... and this will be on your Brain Dump!! Don't let the order of the terms fool you. The slope of this function is -30 ... get it?

• Jefferson starts with $550 in his bank account and takes out $30 each week.

• Jefferson starts with $30 in his bank account and withdraws $550.

• Jefferson starts with 30 pieces of candy ate 550 pieces.

• Jefferson starts with 550 pieces of candy ate 30 pieces.

Answer explanation

y = 550 - 30x

The answer was

"Jefferson starts with $550 in his bank account and takes out $30 each week."

Jefferson must have had a balance of 550 to start ... when he "takes out" or withdrawals $30 per week ... the balance in the account is changing by - 30 each week ... m = -30

Notice that only this answer needed a variable ... it was the only once that talked about money coming out "each week" ... which is the same thing as "per week"

Tags

CCSS.HSF.LE.B.5

Which sentence is represented by the function  y = 175 - 5x?

Hey....I've been preaching y = mx + b ... and this will be on your Brain Dump!! Don't let the order of the terms fool you. The slope of this function is -5 ... get it?

• Mr. Rose collected 175 pieces of candy trick-or-treating and eats 5 pieces

• Mr. Rose collected 175 pieces of candy trick-or-treating and eats 5 pieces each day

• Mr. Rose collected 175 pieces of candy trick-or-treating and buys 5 more pieces

• Mr. Rose collected 5 pieces of candy trick-or-treating and eats 175 pieces

Answer explanation

y = 175 - 5x

Yes...I collected 175 pieces of candy and eat 5 each day.

Since there was 175 pieces of candy in my bucket, that is my b.

Notice that only this answer needed a variable ... it was the only once that talked about candy being eaten "each day" ... which is the same thing as "per day"

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2