Question

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 1

y = 1164x + 14,242

Explanation:

Answer 2

`y = 1164x + 14242`

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:

`(x_1,y_1) = (2,16570)`

`(x_2,y_2) = (22,39850)`

Determine the slope.

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (39850 -16570)/(22 - 2)`

`m = (23280)/(20)`

`m = 1164`

The equation is calculated using:

`y - y_1 = m(x - x_1)`

Where

`m = 1164`

`(x_1,y_1) = (2,16570)`

So,

`y - y_1 = m(x - x_1)`

`y - 16570 = 1164(x - 2)`

`y - 16570 = 1164x - 1164*2`

`y - 16570 = 1164x - 2328`

Add 16570 to both sides

`y - 16570 + 16570 = 1164x - 2328 + 16570`

`y = 1164x - 2328 + 16570`

`y = 1164x + 14242`