Answer:
L(13) = 200
Step-by-step explanation:
Linear function:
A linear function has the following format:
[tex]y = mx + b[/tex]
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: [tex]m = \frac{50}{4} = 12.5[/tex]
So
[tex]y = 12.5x + b[/tex]
L (5) = 100
So [tex]y(5) = 100[/tex], which means that when [tex]x = 5, y = 100[/tex], and we use this to find b.
[tex]y = 12.5x + b[/tex]
[tex]100 = 12.5*5 + b[/tex]
[tex]b = 100 - 12.5*5[/tex]
[tex]b = 37.5[/tex]
So
[tex]L(x) = 12.5x + 37.5[/tex]
a. Determine the value of L (13)
L when [tex]x = 13[/tex]. So
[tex]L(13) = 12.5*13 + 37.5 = 200[/tex]
