How Do I Prove L(x) = ax for All x in R1 Using Linear Operator Properties?

[mpm]

I have another problem that I am needing a little guidance.

Problem:
Let L be a linear operator on R1 and let a = L(1). Show that L(x) = ax for all x belongs to set R1.

Do i just need to use the definition of a linear transformation and show that this is a linear transformation or what?

 

[TD]

Do i just need to use the definition of a linear transformation and show that this is a linear transformation or what?

Not to "show it is a lineair transformation" because that is already given. But because it is given, you can use its definition on L to prove what is stated