Question

What linear function has f(0) = 5 and f(7) = 12?

Answer 1

Answer: f(x) = x + 5

Step-by-step explanation:

Every real valued linear function is of the form

$f(x)=ax+b$, where a≠0 and a, b ∈R

For the given function,

$f(0)=5$

⇒$a(0)+b=5$

⇒$b=5$

Further,

$f(7)=12$

⇒$7a+5=12$

⇒$a=1$

Hence, the required function is f(x)=x + 5

Answer 2

Remember that the formula for a line in Slope-Intercept form is:    y = mx + b

   where  m = slope

              b = y-intercept    (the point where x=0)

 

The y-intercept is given:    the point (0,7)

 

The slope is rise / run   =   (12-7) / (2-0)  =   5/2

 

The equation is:

     f(x) = (5/2)x + 7

 

Check:

  is f(0) = 7  

    f(0) = (5/2)(o) + 7  

    f(0) = 7  

 

  Is f(2) = 12  

   f(2) = (5/2)(2) + 7  

   f(2) = 5 + 7  

   f(2) = 12