Question

1. the table below shows the sales for a flower company for the years 2007 through 2012. answer the given questions about this table on your answer sheet.

a) graph the data on the scatter plot and draw a line of best fit for the data.
flower sales

year	sales (in thousands)
2008	$330
2009	$345
2010	$370
2011	$395
2012	$420

b) write an equation for the line of best fit for this data. let x represent the years since 2007 and y represent the sales, in thousands of dollars.
c) according to your equation, in what year will the sales reach about $500 (in thousands)? use mathematics to explain how you determined your answer.

1. mr. van made a graph to represent the time his students spent studying for their test and their actual test score. which is the correct equation for the line of best fit?

a) y = 1.4x + 55
b) y = 1.4x - 84
c) y = 0.72x + 60
d) y = 0.72 + 56
(graph with points (7, 65) and (25, 90), x-axis: hours of study, y-axis: test scores (%))

1. which relationship is shown by this scatter plot?

(scatter plot: x-axis: cost of a gym membership, y-axis: number of new gym memberships sold, points show a negative trend)
a) as the cost goes down, the number sold goes down.
b) as the cost goes up, the number sold goes down.
c) as the cost does down, the number sold remains the same.
d) there is no relationship between cost and the number sold.

Explanation:

Question 11

Step1: Calculate the slope

We have two points \((7, 65)\) and \((25, 90)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{90 - 65}{25 - 7}=\frac{25}{18}\approx1.4\).

Step2: Use point - slope form to find the equation

Using the point \((7, 65)\) and \(m = 1.4\), the point - slope form is \(y - y_1=m(x - x_1)\). So \(y-65 = 1.4(x - 7)\).
Expanding, \(y-65=1.4x-9.8\), then \(y = 1.4x+65 - 9.8=1.4x + 55.2\approx1.4x + 55\).

Looking at the scatter plot, as the cost of a gym membership (x - axis) increases, the number of new gym memberships sold (y - axis) decreases. This shows a negative correlation. Option A says as cost goes down, number sold goes down (positive correlation, wrong). Option C says number sold remains same (wrong). Option D says no relationship (wrong). Option B says as cost goes up, number sold goes down (correct).

Answer:

A. \(y = 1.4x+55\)

Question 12