The scatterplot below shows the relationship between the
number of hot dogs left over after the cook-out and the number
of people who attended a cook-out.

Based on the trend line, approximately how many hot dogs would be remaining if only 18 people attended the cook out?

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MrRoyal MrRoyal · Answer 1 · 2021-11-05T20:28:13+01:00

A trend line is drawn through the points of a scatter plot

There would be 7 hot dogs remaining, when 18 people attended the cook out.

The points on the trend line are:

[tex]\mathbf{(x,y) = (0,60)(2,54)}[/tex]

The slope of the trend line is:

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 -x_1}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{54 - 60}{2 -0}}[/tex]

[tex]\mathbf{m =- \frac{6}{2}}[/tex]

[tex]\mathbf{m = -3}[/tex]

When x = 18, we have (18,y):

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 -x_1}}[/tex] becomes

[tex]\mathbf{-3 = \frac{55 - y}{2 -18}}[/tex]

[tex]\mathbf{-3 = \frac{55 - y}{-16}}[/tex]

Multiply both sides by 16

[tex]\mathbf{48 = 55 - y}[/tex]

[tex]\mathbf{y = 55 - 48}[/tex]

[tex]\mathbf{y = 7}[/tex]

Hence, there would be 7 hot dogs remaining, when 18 people attended the cook out.