Math, asked by vipinkumarchauhan157, 1 month ago

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

Answers

Answered by mathdude500
4

\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.

Similar questions