Question

1. sales growth metro department store’s annual sales (in millions of dollars) during the past 5 years were as follows: annual sales, y 5.8 6.2 7.2 8.4 9.0 year, x 1 2 3 4 5 a. plot the annual sales (y) versus the year (x). b. draw a straight line l through the points corresponding to the first and fifth years. c. derive an equation of the line l. d. using the equation found in part (c), estimate metro’s annual sales 3 years from now (x = 8).

Explanation:

Step1: Identify line points

Points: $(x_1,y_1)=(1,5.8)$, $(x_2,y_2)=(5,9.0)$

Step2: Calculate slope $m$

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{9.0-5.8}{5-1}=\frac{3.2}{4}=0.8$

Step3: Find y-intercept $b$

Use $y=mx+b$, substitute $(1,5.8)$:
$5.8=0.8(1)+b \implies b=5.8-0.8=5.0$

Step4: Write line equation

$y=0.8x+5.0$

Step5: Estimate sales at $x=8$

Substitute $x=8$ into equation:
$y=0.8(8)+5.0=6.4+5.0=11.4$

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For parts a and b:

a. Create a coordinate system with x-axis (Year, 1 to 5) and y-axis (Annual Sales, 5 to 9). Plot the points (1,5.8), (2,6.2), (3,7.2), (4,8.4), (5,9.0).
b. Draw a straight line connecting the first point (1,5.8) and the fifth point (5,9.0).

Answer:

a. (Plot with points (1,5.8), (2,6.2), (3,7.2), (4,8.4), (5,9.0) on x-y axes)
b. (Straight line connecting (1,5.8) and (5,9.0))
c. $y=0.8x+5$
d. 11.4 million dollars