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50 Points for answers(s):



Based on the graph, what is the initial value of the linear relationship?

−2


0


two over three


3
(Graph at bottom of page)
_____________________________________________________




What is the rate of change for the linear relationship modeled in the table?




x


y




−1 =x

10 =y


1= x

9 =y


3=x

8 =y


5=x

7 =y


Anegative one over two

B0

Cone over two

D2


________________________________________________________


Which scenario best matches the linear relationship expressed in the equation y = 13.50x + 300?


Bobby has $300 in the yearbook fund and spends $13.50 on each yearbook.


Bobby has $13.50 in the yearbook fund and spends $300 on each yearbook.


Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.


Bobby has $13.50 in the yearbook fund and earns $300 for each yearbook sold.

________________________________________________________________



Which scenario best matches the linear relationship shown in the table?



Weeks


Dollars




0= weeks

10 = dollars


2= weeks

20 = dollars


4= weeks

30 = dollars


6= weeks

40 = dollars

____________________________________________________________



Shanna had $10 in her piggy bank and earned $10 each week in allowance.


Shanna had $10 in her piggy bank and earned $5 each week in allowance.


Shanna had $10 in her piggy bank and spent $5 each week on stickers.


Shanna earns $10 each week.


___________________________________________________________



Kenny has $1,400 in the bank. He earns $150 every week at his after-school job. What is the rate of change for the scenario described?


2


150


300


1400

50 Points for answers(s): Based on the graph, what is the initial value of the linear relationship? 2 0 two over three 3 (Graph at bottom of page) What is the r class=

Verified Answer :

dalendrk

Q1.
The initial value of the linear relationship is -2    /y-intercept/

Answer: -2.

Q2.  /The slope of a
line is a rate of change./
x = -1 and y = 10
x = 1 and y = 9

(10 - 9)/(-1 - 1) = -1/2

Answer: A. -1/2.

Q3.
y = 3.50x + 300

Answer: Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.


Q4.
y = mx + b
(0; 10); (2; 20)

m = (20 - 10)/(2 - 0) = 10/2 = 5
(0; 10) ⇒ b = 10

y = 5x + 10

Answer: Shanna had $10 in her piggy bank and earned $5 each week in allowance.


Q5. /The slope of a
line is a rate of change./

 y = 150x + 1,400

Answer: 150.

Answer:

Ques 1)

            -2

Ques 2)

     A. negative one over two

Ques 3)

Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.

Ques 4)

she initially had $ 10 in her piggy bank and also she earned $ 10 each week in allowance.

Ques 5)

              150

Step-by-step explanation:

Ques 1)

We know that the initial value of the linear relationship is the y-value when x=0.

i.e. x=0 is considered as the initial case.

Hence, when x=0 we have ,

y= -2

    Hence, the initial value is:

                         -2

Ques 2)

We are given a table as:

                x                y

               -1                10

                1                  9

                3                 8

                5                 7

As we know that a linear function has a constant rate.

Hence we calculate rate of change from x= -1 to x=1

We know that the rate of change of a function from x=a to x=b is calculated as:

\(Rate=\dfrac{f(b)-f(a)}{b-a}\)

Hence, when a= -1 and b=1 the rate of change is:

\(Rate=\dfrac{f(1)-f(-1)}{1-(-1)}\\\\\\Rate=\dfrac{9-10}{1+1}\\\\\\Rate=\dfrac{-1}{2}\)

Hence, option A is correct.

A. negative one over two.

Ques 3)

The linear relationship is given by:

y = 13.50x + 300

Hence, this means that for each yearbook  he earns $ 13.50.

Also, when x=0

we have y=300

This means that Bobby has $ 300 in the yearbook fund.

Hence, the best statement is:

Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.

Ques 4)

     Weeks          Dollars

         0                  10

        2                  20

        4                  30

        6                  40

This means that she initially had $ 10 in her piggy bank and also she earned $ 10 each week in allowance.

Since the function is a linear function as the rate is constant and could be modeled as:

            y=10x+10

where x are the number of weeks and y is the cost in dollars.

Ques 5)

It is given that:

Kenny has $1,400 in the bank. He earns $150 every week at his after-school job.

Let x denote the number of weeks and y denotes the amount in his bank.

This means that with the information we can modeled the function as:

                        \(y=150x+1400\)

we know that for any equation of the type y=mx+c

m represents the rate of change or slope of the linear function and c denote the initial value of the function.

Hence here we have:  m=150

Hence, rate of change is:150

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