Question

1. what type of association is shown by the data in the scatter plot?

a positive association
b negative association
c no association
d trend association

1. which equation best models the data shown in the scatter plot?

a y = x - 3
b y = x - 5
c y = 3x - 3
d y = 3x - 5

1. when hana goes to the mall, she always buys the same lunch and also buys some books. the table shows the number of books she buys x and the total amount of money she spends y. make a scatter plot of the data. tell whether there is a positive correlation, a negative correlation, or no correlation. then, if possible, draw a trend line.

x	1	2	2	3	4
y	17	21	23	26	34

correlation: positive

1. which statements about the trend line in item 3 are true? select all that apply.

a the slope is the cost of one book.
b the slope is the cost of hanas lunch.
c the y - intercept is the cost of one book.
d the y - intercept is the cost of hanas lunch.

1. hana draws a trend line for the scatter plot in item 3 and writes the equation y = 5.5x + 11 to represent the line. use her equation to predict how much she will spend if she buys 8 books.

Explanation:

Step1: Analyze scatter - plot in question 1

As the x - values increase, the y - values also increase, so it is a positive association.

Step2: Analyze scatter - plot in question 2

We can check by substituting points. Let's assume a point \((2,1)\) (from the scatter - plot).
For \(y = x-3\), when \(x = 2\), \(y=2 - 3=-1
eq1\).
For \(y = x - 5\), when \(x = 2\), \(y=2 - 5=-3
eq1\).
For \(y = 3x-3\), when \(x = 2\), \(y=3\times2 - 3=3
eq1\).
For \(y = 3x - 5\), when \(x = 2\), \(y=3\times2 - 5=1\). So \(y = 3x - 5\) best models the data.

Step3: Analyze data in question 3

As the number of books \(x\) increases, the total amount of money \(y\) increases, so there is a positive correlation.

Step4: Analyze trend - line in question 4

The equation of a line is \(y=mx + b\) where \(m\) is the slope and \(b\) is the y - intercept. In the context of the cost problem (\(y\) is total cost and \(x\) is number of books), the slope \(m\) is the cost of one book and the y - intercept \(b\) is the fixed cost (cost of lunch). So A and D are true.

Step5: Solve question 5

Substitute \(x = 8\) into \(y=5.5x + 11\).
\(y=5.5\times8+11\)
\(y = 44+11\)
\(y = 55\)

Answer:

1. A. positive association
2. D. \(y = 3x - 5\)
3. positive correlation
4. A. The slope is the cost of one book; D. The y - intercept is the cost of Hana's lunch
5. 55