Question

PLS I NEED HELP

2. Write the rule for the linear function. Remember a function rule is written using f(x).

Answer 1

`f(x) = (1)/(2)x + 5`

Explanation:

So you can generally express a linear function use the slope-intercept form as such:
`y=mx+b` where m=slope, and b=y-intercept.

The y-intercept is defined as the value of f(0), since when the line crosses the y-axis, the x-value is 0, and as provided in the table that value is 5, so we have the function rule:
`f(x) = mx+5`

The slope is defined as how much y-changes, as x increases by 1. We can generally use the formula:
`m=(y_2-y_1)/(x_2-x_1)` and this can be found using any two points, since the slope is constant.

We can use the two points (0, 5) and (2, 6) and plug it into the equation, to find the rise/run

`(6-5)/(2-0) = (1)/(2)`

So plugging this into the slope-intercept form you get the function

`f(x) = (1)/(2)x + 5`