Question

Some values of the linear function f are given in the table shown. What is the value of f(100)?

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Answer 1

f(100) = 160.

Explanation:

Linear function:

The equation of a linear function has the following format:

`y = mx + b`

In which m is the slope(how much f(x) changes when x changes by 1) and b is the y-intercept(value of f(x) when x = 0).

Finding the slope:

Suppose we have two points. The slope is the change in the output divided by the change in the input.

In this question, we have points (45,50) and (60,80).

Change in the output: 80 - 50 = 30

Change in the slope: 60 - 45 = 15

Slope: 30/15 = 2

So

`y = 2x + b`

Point (45,50)

This means that when
`x = 45, y = 50`. We use this to find the value of b.

`y = 2x + b`

`50 = 2(45) + b`

`b = -40`

So

`y = 2x - 40`

With y = f(x)

What is the value of f(100)?

This is y when x = 100. So

`f(100) = 2(100) - 40 = 200 - 40 = 160`

f(100) = 160.