Question

The number of exports is shown as g(x). Use the data in the table below, representing both functions, to explain to your boss the solution to the system of equations and what that solution represents. Use complete sentences.

Month f(x) = Number of imports g(x) = Number of exports
January (1) 3 1
February (2) 4 3
March (3) 5 5
April (4) 6 7

Answer 1

Explanation:

Given the table:

Month f(x) = Number of imports g(x) = Number of exports

January (1) 3 1

February (2) 4 3

March (3) 5 5

April (4) 6 7

From the table, it is clear that:

Number of imports = number of month + 2

so

`f(x) = x + 2`

also

Number of exports = 2(number of month) + 1

so

`g(x) = 2x - 1`

Therefore, number of imports equals the number of month plus one. i.e.
`f(x) = x + 2`, which is a linear function.

If we compare it with slope-intercept form of the line

`y=mx+b`

Then,

slope = m = 1

y-intercept = 2

Also number of exports equals is also a linear function.

i.e.
`g(x) = 2x - 1`

Here,

slope = m = 2

y-intercept = -1