Answer:
The base fee is 5
Step-by-step explanation:
Linear Function
The linear function is widely used to model real situations in life where the dependancy of one variable are linear by nature.
The problem gives us three conditions, more than enough to find a linear model for the earnings for running errands. Let's make x the number of hours it takes to run the errands, and y the earnings. The linear model has the general equation
[tex]y=mx+b[/tex]
We have these points (1,20) (2,35) (3,50) and need to find the base fee, which is the value of b or the independant term of the equation.
We'll use the first two points to find the equation and the third point to verify it. Using (1,20)
[tex]20=1\cdot m+b[/tex]
[tex]m+b=20[/tex]
Now we use (2,35)
[tex]35=m\cdot 2+b[/tex]
[tex]2m+b=35[/tex]
Subtracting both equations
[tex]m=15[/tex]
Replacing into the first equation
[tex]b=5[/tex]
The equation is
[tex]y=15x+5[/tex]
Let's test the formula by replacing the point x=3
[tex]y=15\cdot 3+5=50[/tex]
The model is accurate and the base fee is 5
