Chapter 3.1, Problem 63HP

To determine

To write: Give an example of a linear equation of the form $Ax+By=C$ for the condition

  $C=0$ and describe the graph of the equation .

Answer to Problem 63HP

The required answer is: Linear equation $2x+4y=0$

Explanation of Solution

Given information:

The given equation form is $Ax+By=C$

The given condition is $C=0$

Calculation:

Example of a linear equation is $2x+4y=0$

The domain is all real numbers which can be selected to make a table. Then create ordered pairs of domain and range. Range is also all real numbers.

$x$	$y$	$(x,y)$
$1$	$-\frac{1}{2}$	$(1,-\frac{1}{2})$
$-1$	$\frac{1}{2}$	$(-1,\frac{1}{2})$

When x is 1 the value of y will be:

  $\begin{array}{l}2(1)+4y=0\\ 2+4y-2=-2\end{array}$

(Subtracting 2 from both sides)

  $\begin{array}{l}4y=-2\\ \frac{4y}{4}=\frac{-2}{4}\end{array}$

(Dividing 4 from both sides)

  $y=-\frac{1}{2}$

(Simplify)

When x is -1 the value of y will be:

  $\begin{array}{l}2(-1)+4y=0\\ -2+4y+2=2\end{array}$

(Adding 2 on both sides)

  $\begin{array}{l}4y=2\\ \frac{4y}{4}=\frac{2}{4}\end{array}$

(Dividing 4 from both sides)

  $y=\frac{1}{2}$

(Simplify)

Therefore plot the points on the graph and then draw a line through them as follows: