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

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:f = \{(1,4),(2,5),(3,6),(4,k) \}$

$\rm :\longmapsto\:Let \: linear \: function \: be \: f(x) =y = ax + b - - (1)$

$\rm :\longmapsto\:(1,4) \in \: f \:$

$\rm :\implies\:a + b = 4 - - - (2)$

Also,

$\rm :\longmapsto\:(2,5) \in \: f$

$\rm :\implies\:2a + b = 5 - - - (3)$

On Subtracting equation (1) from equation (2), we get

$\rm :\implies\:a = 1$

On substituting a = 1, in equation (1), we get

$\rm :\longmapsto\:1 + b = 4$

$\rm :\implies\:b = 3$

$\bf \: \therefore \: linear \: function \:, \: f(x) = y = x + 3$

$\rm :\longmapsto\:As \: (4,k) \in \: f$

$\rm :\implies\:k \: = \: 4 + 3$

$\bf\implies \:k = 7$

Additional Information :-

• Linear functions are those functions whose graph is a straight line.

• A linear function is of the form y = f(x) = a + bx.

• A linear function has one independent variable and one dependent variable.

• The independent variable is x and the dependent variable is y.