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

A. negative one over two

B. 0

C. one over two

D. 2

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

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.

virtuematane virtuematane · Answer 2 · 2019-04-26T08:38:08+02:00

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:

[tex]Rate=\dfrac{f(b)-f(a)}{b-a}[/tex]

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

[tex]Rate=\dfrac{f(1)-f(-1)}{1-(-1)}\\\\\\Rate=\dfrac{9-10}{1+1}\\\\\\Rate=\dfrac{-1}{2}[/tex]

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:

[tex]y=150x+1400[/tex]

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