Chapter 3.2, Problem 49HP

To determine

To write: A linear equation of the form $y=mx+c$ that has a root of $-\frac{3}{4}$ and also to write its related function.

Answer to Problem 49HP

Linear equation $4y-4x=3$ and its related function is written as, $f\left(x\right)=x+\frac{3}{4}$ .

Explanation of Solution

Given information: Any linear equation with its root as $-\frac{3}{4}$ .

Formula/Concept used: Zero of a function is the value of its independent variable when the value of the function is 0. Or to get the zero, y is put equal to zero and equation is then solved for x .

Calculation: As it is given that its one root is $-\frac{3}{4}$ , so,

  $\begin{array}{l}x=-\frac{3}{4}\\ x+\frac{3}{4}=0\\ x=\frac{212}{0.00177}=119774\end{array}$

And its corresponding linear equation is then written as:

  $\begin{array}{l}x+\frac{3}{4}=y\\ \Rightarrow \frac{4x+3}{4}=y\\ \Rightarrow 4x+3=4y\\ \Rightarrow 4y-4x=3\end{array}$

Conclusion: So, required linear equation is $4y-4x=3$ and its related function in form $y=f(x)$ will be written as $f\left(x\right)=\frac{4x+3}{4}$ .