The scatter plot below shows the amount of profit earned per month by a bagel shop over a period of 11months.
10
.
Profit in Thousands, p

0 1 2 3 4 5 6 7 8 9 10 11 12
Month, m
Write an equation for the line of best fit that models the relationship between profit in thousands, p, and time in months,
m. Then, use your equation to predict the profit the bagel shop will earn in month 12. Round slope and y-intercept to the
nearest tenth.

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MrRoyal MrRoyal · Answer 1 · 2022-03-02T10:48:55+01:00

Scatter plots are used to illustrate the correlation between the x and y variables

From the scatter plot, we have the following ordered pairs

(x,y) = (2,3) and (8,7)

Start by calculating the slope (m) using:

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

So, we have:

[tex]m = \frac{7 - 3}{8 - 2}[/tex]

Evaluate the differences

[tex]m = \frac{4}{6}[/tex]

Divide

[tex]m = 0.7[/tex]

The equation is then calculated as:

[tex]y = m(x -x_1) + y_1[/tex]

So, we have:

[tex]y = 0.7(x -2) + 3[/tex]

Expand

[tex]y = 0.7x -1.4+ 3[/tex]

[tex]y = 0.7x + 1.6[/tex]

When x = 12, the equation becomes

[tex]y = 0.7* 12 + 1.6[/tex]

[tex]y = 10[/tex]

Hence, the bagel shop will earn $10,000 in month 12