Question

Find a linear equation satisfying the followingf(2)= 21 and f(-4) = -15f(x) =help (formulas)

Answer 1

Recall

f(x)=y

Given

f(2)= 21 and f(-4) = -15

f(x) =

Step 1

$\begin{gathered} y=mx+b \\ \text{when} \\ f(2)=21_{} \\ 21=2m+b\ldots\text{Equation (i)} \end{gathered}$$\begin{gathered} y=mx+b \\ \text{when } \\ f(-4)=-15 \\ -15=-4m+b\ldots\text{Equation (i}i) \end{gathered}$

Step 2

Let's solve equation (i) and Equation (ii) simultaneously

$\begin{gathered} 21=2m+b\ldots(i) \\ -15=-4m+b\ldots(ii) \\ In\text{ equation (i) Let's make b the subject} \\ b=21-2m \end{gathered}$$\begin{gathered} we\text{ now substitute in equation (i}i) \\ -15=-4m+21-2m \\ \text{collect the like terms} \\ -15-21=-4m-2m \\ -36=-6m \\ \text{Divide both sides by -6} \\ -\frac{36}{6}=-\frac{6m}{-6} \\ \\ m=6 \end{gathered}$

Step 3

$We\text{ can substitute for m either in equation(i) or (i}i)$

using Equation (ii)

$\begin{gathered} -15m=-4m+b \\ -15=-4(6)+b \\ \text{collect the like terms} \\ -15=-24+b \\ \text{collect the like terms} \\ -15+24=b \\ b=9 \end{gathered}$

Step 4

M= 6 and b= 9

$\begin{gathered} We\text{ can substitute into y=mx+b} \\ y=6x+9 \end{gathered}$

The linear equation is

$y=6x+9$