The equation, y = 1250x + 22,850, gives the salary of a person as "y" after the stated number of years (x). Model the data with a linear function using the points (1, 24,100) and (3, 36,600) Then use this function to predict the salary in 5 years.

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MrRoyal MrRoyal · Answer 1 · 2021-03-27T07:16:22+01:00

Answer:

(a) [tex]y = 6250x +17850[/tex] --- The function

(b) [tex]y = 49100[/tex] --- The salary in 5 years

Step-by-step explanation:

Given

[tex]y = 1250x + 22850[/tex]

Solving (a): Model the function around (1,24100) and (3,36600)

First, we calculate the slope

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

[tex]m = \frac{36600 - 24100}{3 - 1}[/tex]

[tex]m = \frac{12500}{2}[/tex]

[tex]m = 6250[/tex]

The function is then calculated as:

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

[tex]y = 6250(x - 1) + 24100[/tex]

[tex]y = 6250x - 6250 + 24100[/tex]

[tex]y = 6250x +17850[/tex]

Solving (b): Salary in 5 years

Here:

[tex]x = 5[/tex]

So:

[tex]y = 6250x +17850[/tex]

[tex]y = 6250*5 +17850[/tex]

[tex]y = 49100[/tex]