Question

Write a linear function f with the values f(0)=-5 and f(1)=-3

Answer 1

Answer: f(x)  = ax + b;

f(0) = -5;

a·0 + b = -5;

b = -5;

f(1) = -3;

a·1 + (-5) = -3;

a - 5 = -3;

a = 5 - 3;

a = 2;

f(x) = 2x - 5;

Step-by-step explanation:

Answer 2

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{f(0) \: = - \: 5} \\ &\sf{f(1) \: = \: - \: 3} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\sf{linear \: function \: f(x)}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

$\begin{gathered}\begin{gathered}\bf  Let :-  \begin{cases} &\sf{f(x) \: = \: ax \: + \: b}  \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\bf\red{Now,}\end{gathered}$

$\tt \:  \longrightarrow \: f(0) = - 5$

$\tt \:  \longrightarrow \: a \times 0 \: + \: b \: = - 5$

$\tt\implies \: \boxed{ \purple{\bf \:  b \: = - \: 5}}$

$\begin{gathered}\bf\red{Now,}\end{gathered}$

$\tt \:  \longrightarrow \: f(1) = - \: 3$

$\tt \:  \longrightarrow \: a \times 1 + b \: = - \: 3$

$\tt \:  \longrightarrow \: a \: - \: 5 = \: - \: 3$

$\tt\implies \: \boxed{ \purple{\tt \:  a \: = \: 2}}$

$\large{\boxed{\boxed{\bf{Hence, f(x) = 2x -5 }}}}$