Respuesta :
Answer:
The value of n is:
13
Step-by-step explanation:
We are given a linear function f(x).
Also we are given a set of values for the function f(x) at different values of x.
The table of values are as follows:
x f(x)
3 7
7 n
9 16
16 26.5
Now, firstly we will find the equation of a line and then put the value of x=7 to find the value of n.
As we know that the equation of a line passing through two point (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
So, let:
(a,b)=(3,7) and (b,d)=9,16)
Hence, then equation of line i.e. y=f(x) is:
[tex]y-7=\dfrac{16-7}[9-3}\times *(x-3)\\\\y-7=\dfrac{3}{2}\times (x-3)\\\\y-7=\dfrac{3}{2}x-\dfrac{9}{2}\\\\y=\dfrac{3}{2}x-\dfrac{9}{2}+7\\\\y=\dfrac{3}{2}x+\dfrac{5}{2}[/tex]
Now, the value of y=f(x) when x=7 is:
[tex]y=\dfrac{3}{2}\times 7+\dfrac{5}{2}\\\\y=\dfrac{21}{2}+\dfrac{5}{2}\\\\y=\dfrac{21+5}{2}\\\\y=\dfrac{26}{2}\\\\y=13[/tex]
Hence, the value of n is:
n=13
