Chapter 3.1, Problem 5BCYP

To determine

Graph each equation by making a table.

Answer to Problem 5BCYP

This a graph parallel to y − axis.

Explanation of Solution

Given:

The equation: $x=3$

Concept Used:

The equation of line parallel to y-axis:

Let AB be a straight line parallel to y-axis at a distance $\text{a}$ units from it. Then, clearly, all points on the line AB have the same x − value is $\text{a}$ .

Thus, AB can be considered as the locus of a point at a distance $\text{a}$ from y-axis and all points on the line AB satisfy the condition $\text{x}\text{=}\text{a}$ .

Thus, if P(x, y) is any point on AB, then $\text{x}\text{=}\text{a}$ .

Hence, the equation of a straight line parallel to y-axis at a distance a from it is x=a

To graph the equation make y as subject and make a table by choosing random value of y and find the corresponding value of x.

Calculation:

Step 1: in this equation $x=3$ y is not present. We can rewrite the equation as $x+0·y=3$

Take random value of y and find the value of corresponding x

Make a table:

y	$x+0·y=3$	(x, y)
– 4	$\begin{array}{l}x+0·y=3\\ x+0·-4=3\\ x=3\end{array}$	$(3,-4)$
– 2	$\begin{array}{l}x+0·y=3\\ x+0·-2=3\\ x=3\end{array}$	$(3,-2)$
0	$\begin{array}{l}x+0·y=3\\ x+0·0=3\\ x=3\end{array}$	$(3,0)$
2	$\begin{array}{l}x+0·y=3\\ x+0·2=3\\ x=3\end{array}$	$(3,2)$

The points are: $(3,-4);(3,-2);(3,0);(3,2)$

Graph of the equation: $x=3$, this is a line parallel to y − axis.

  

Thus, the points on the graph are: $(3,-4);(3,-2);(3,0);(3,2)$ for the equation $x=3$