Question

Given that L is a linear function, L (5) = 100 and L (9) = 150.

a. Determine the value of L (13)

Answer 1

L(13) = 200

Explanation:

Linear function:

A linear function has the following format:

`y = mx + b`

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

Finding the slope:

L (5) = 100 and L (9) = 150.

The slope is given by the change in the output(L, which is equals to y in the general formula) divided by the change in the input(x).

Change in the output: 150 - 100 = 50

Change in the input: 9 - 5 = 4

Slope:
`m = (50)/(4) = 12.5`

So

`y = 12.5x + b`

L (5) = 100

So
`y(5) = 100`, which means that when
`x = 5, y = 100`, and we use this to find b.

`y = 12.5x + b`

`100 = 12.5*5 + b`

`b = 100 - 12.5*5`

`b = 37.5`

So

`L(x) = 12.5x + 37.5`

a. Determine the value of L (13)

L when
`x = 13`. So

`L(13) = 12.5*13 + 37.5 = 200`