Answer:
[tex]f(x) = x + 4[/tex]
Step-by-step explanation:
First, recognise the form
[tex]y = mx + c[/tex]
where m is the slope, c is the constant, and y is f(x).
Then we use this formula:
[tex]y - y1 = ( \frac{y2 - y1}{x2 - x1} )(x - x1)[/tex]
We choose two points from the table: (2,6) and (4,7), then we substitute:
[tex](y - 6) = ( \frac{7 - 6}{4 - 2} )(x - 2)[/tex]
Solve as it is:
[tex](y - 6) = 1(x - 2) \\ y - 6 = x - 2 \\ y = x - 2 + 6 \\ y = x + 4[/tex]
which is the same as
[tex]f(x) = x + 4[/tex]
