Chapter 3.1, Problem 61HP

To determine

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

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

Answer to Problem 61HP

The required answer is: Linear equation $4y=12$

Explanation of Solution

Given information:

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

The given condition is $A=0$

Calculation:

Example of a linear equation is $4y=12$

With condition $A=0$ , the equation with form $Ax+By=C$ will be:

  $\begin{array}{l}(0)x+4y=12\\ 0+4y=12\\ 4y=12\end{array}$

(Simplify)

Here x-intercept is 0 since $A=0$ therefore the line will be a horizontal line on the graph.

To find y-intercept, let $x=0$

  $\begin{array}{l}0+4y=12\\ 4y=12\\ \frac{4y}{4}=\frac{12}{4}\end{array}$

(Divided by 4 on both sides)

  $y=3$

(Simplify)

Therefore y-intercept is 3, the line will intersect y-axis at (0, 3) on the graph.

Graph as shown below: