Question

Let f = {(1,4), (2,5), (3,6), (4, k) is a
linear function then find the function and
the value of k.​

Answer 1

Answer:

ans is 7

hope u find it helpful

Answer 2

The function is $f(x)=x+3$  and the value of k is 7.

Step-by-step explanation:

Given:

f = {(1,4), (2,5), (3,6), (4, k)} is a linear function.

To Find:

The function and the value of k.

Solution:

As given- f = {(1,4), (2,5), (3,6), (4, k)} is a linear function.

f is linear function.

Let $f(x)= y =mx+c$

For (1,4)

Putting value of (1,4) in equation $f(x)= y =mx+c$.

$y=mx+c$

$4=m\times1+c$

$m+c=4$  ----------- equation no.01.

For (2,5)

Putting value of (2,5) in equation $f(x)= y =mx+c$.

$y=mx+c\\5=m\times2+c\\2m+c=5$   ---------- equation no.02.

Substracting equation no.01 from equation no.02.

$m=1$

Putting the value of m=1 in equation no.01.

$1+c=4\\c=3$

Putting the value of m and c in  $f(x)= y =mx+c$.

$f(x)= y =mx+c$

              $= 1\times x + 3$

       $f(x)=y= x+3$

For (4,k)

Putting value of (4,k) in equation $f(x)=y= x+3$.

$y=x+3\\k=4+3\\k=7$

Thus,the function is $f(x)=x+3$  and the value of k is 7.