Meg plotted the graph below to show the relationship between the temperature of her city and the number of sweaters sold at a store:

Main title on the graph is Sweater Sale. Graph shows 0 to 30 on x axis at increments of 5 and 0 to 12 on y axis at increments of 1. The label on the x axis is Temperature in degree C, and the label on the y axis is Number of Sweaters Sold. Dots are made at the ordered pairs 0, 12 and 2.5, 10 and 2.5, 11 and 5, 10 and 7.5, 9 and 7.5, 10 and 10, 7 and 12.5, 6 and 12.5, 8 and 15, 4 and 15, 7 and 17.5, 5 and 20, 1 and 20, 3 and 22.5, 9 and 25, 1 and 27.5, 1.

Part A: In your own words, describe the relationship between the temperature of the city and the sale of sweaters in the city. (5 points)

Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)

Solution:  

The description about the graph is:  

Graph shows 0 to 30 on x axis at increments of 5 and 0 to 12 on y axis at increments of 1. The label on the x axis is Temperature in degree C, and the label on the y axis is Number of Sweaters Sold. Dots are made at the ordered pairs 0, 12 and 2.5, 10 and 2.5, 11 and 5, 10 and 7.5, 9 and 7.5, 10 and 10, 7 and 12.5, 6 and 12.5, 8 and 15, 4 and 15, 7 and 17.5, 5 and 20, 1 and 20, 3 and 22.5, 9 and 25, 1 and 27.5, 1.  

Part A:  The relationship between the temperature of the city and the sale of sweaters in the city can be found by drawing the line of best fit.  

If you will draw line through , (12.5,6) and (15,4), it will best represent line of best fit, because most of points on same and opposite side of line are equidistant from each other.

Equation of line passing through two points,[tex](x_{1},y_{1}),(x_{2},y_{2})is, \frac{y-y_{1} }{x-x_{1} } = \frac({y_{2} - y_{1}})({x_{2}-x{1} })[/tex]

Equation of line passing through (12.5,6) and (15,4) is given by

[tex]\frac{y-6}{x-12.5} = \frac{6-4}{12.5-15}[/tex]

[tex]2x-25=-2.5+15[/tex]

[tex]2x+2.5y=40[/tex]

[tex]20x+25y= 400[/tex]

[tex]4x+5y=80[/tex]

Part B: Description of line of best fit  

A line of best is the line which passes through all or some points or only through a single point, which describes the relationship between x and y values of data set. The line passes through (12.5,6), (15,4),and (7,10) that is three points.  

(C) 4 x + 5 y=80  

5 y= - 4 x +80

[tex]y=\frac{-4x}{5}+16[/tex]

Slope [tex]= \frac{-4}{5}[/tex], Y- intercept = 16

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