The table below shows the average annual salary of the workers at the Pearson
Corporation over the course of time since 1980. Let x represent the number of years
since 1980 with x = 0
representing the year 1980. Let y represent the average annual
salary of the workers. Complete the slope-intercept form of the equation for the line of
best fit below with the appropriate value for the slope.

Answer:

[tex]y = 1164x + 14242[/tex]

Step-by-step explanation:

From the question, we understand that

x = 0, when year = 1980

First, we need to determine the slope of the table.

Pick any two corresponding values of year and average salary

year = 1982, average salary = 16570

year = 2002, average salary = 39850

Convert years to x values

year = 1982 implies that x = 2 i.e. 1982 - 1980

year = 2002 implies that x = 22 i.e. 2002 - 198-

So, we have:

[tex](x_1,y_1) = (2,16570)[/tex]

[tex](x_2,y_2) = (22,39850)[/tex]

Determine the slope.

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

[tex]m = \frac{39850 -16570}{22 - 2}[/tex]

[tex]m = \frac{23280}{20}[/tex]

[tex]m = 1164[/tex]

The equation is calculated using:

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

Where

[tex]m = 1164[/tex]

[tex](x_1,y_1) = (2,16570)[/tex]

So,

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

[tex]y - 16570 = 1164(x - 2)[/tex]

[tex]y - 16570 = 1164x - 1164*2[/tex]

[tex]y - 16570 = 1164x - 2328[/tex]

Add 16570 to both sides

[tex]y - 16570 + 16570 = 1164x - 2328 + 16570[/tex]

[tex]y = 1164x - 2328 + 16570[/tex]

[tex]y = 1164x + 14242[/tex]

Answer:

y = 1164x + 14,242

Step-by-step explanation:

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