Question

L(x) is a linear function. Find L(x), if L(5) = 6 and L(10) = 12

Answer 1

If L(x) is a linear function, then, let L(x) = ax + b.
Now using L(5) and L(10) values find out a and b and you will get your answer.

Answer 2

can you show me an example because im sort of lost

Answer 3

Just put x = 5 in L(x) :

L(5) = a(5) + b

And then put x = 10 in L(x)

L(10) = a(10) + b

Subtract :

L(10) - L(5) = 10a + b - (5a + b)

= \(\left(10a - 5a\right) + \color{blue}{\cancel{b}} - \color{blue}{\cancel{b}}\)
= 5a

And since, it is given to you that L(10) = 12 and L(5) = 6

Therefore, L(10) - L(5) = 6

But from above work, we got L(10) - L(5) = 5a

So, 5a = 6.

And a = ?

Answer 4

Can you solve it now ?

Answer 5

yeah thank you