Answer:
b = 5/4
Step-by-step explanation:
Equations
Given the function:
[tex]f(x)=mx+b[/tex]
It's required to find the value of b such that:
[tex]5f(x)=f(5x)+5[/tex]
Substituting:
[tex]5(mx+b)=5mx+b+5[/tex]
Operating:
[tex]5mx+5b=5mx+b+5[/tex]
Simplifying:
[tex]5b=b+5[/tex]
Subtracting b:
[tex]4b = 5[/tex]
Dividing by 4:
b = 5/4
