Question

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.
if this data were displayed in a scatter plot, select all statements that would be true about a good trend line summarizing the data.
a. the slope approximates the average cost of one book.
b. the slope approximates the cost of hanas lunch.
c. the y - intercept approximates the average cost of one book.
d. the y - intercept approximates the cost of hanas lunch.
e. the trend line goes through the origin.

Explanation:

Step1: Recall the equation of a line

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y -\)intercept. In the context of a cost - related linear model \(y\) (total cost) \(=m\) (cost per item) \(x\) (number of items)+ \(b\) (fixed cost). Here, \(x\) is the number of books and \(y\) is the total amount of money spent.

Step2: Analyze the slope

The slope \(m\) in the line \(y=mx + b\) represents the rate of change. If \(y\) is the total money spent (on books and lunch) and \(x\) is the number of books, the slope \(m\) represents the cost per book (since for each additional book \(x\) increases by 1, and \(y\) changes by the cost of that book).

Step3: Analyze the \(y -\)intercept

The \(y -\)intercept \(b\) is the value of \(y\) when \(x = 0\). When \(x=0\) (Hana buys no books), \(y=b\), which represents the cost of lunch.

Step4: Analyze the trend - line passing through the origin

If the trend - line passed through the origin \((0,0)\), then when \(x = 0\), \(y=0\). But when \(x = 0\), \(y\) should be the cost of lunch (a non - zero value in this context, because she always buys lunch). So the trend - line does not pass through the origin.

Answer:

B. The slope approximates the cost of Hana’s lunch; D. The \(y -\)intercept approximates the cost of Hana’s lunch.