Chapter 12.1, Problem 34STP

To determine

To check: which of the given equation in the option represents a line parallel to the given graph.

Answer to Problem 34STP

F. $x-\frac{1}{3}y=0$ .

Explanation of Solution

Given:

The given graph is $y=3x+6$ .

The given options are:

F. $x-\frac{1}{3}y=0$

G. $y=\frac{1}{3}x+2$

H. $y=-3x+2$

I. $y=-2x+2$

Calculation:

As the given graph of $y=3x+6$ .

Now, to find the slope of the equation. Then,

  $\begin{array}{l}\because y=mx+c\left\{\text{equation of a line}\right\}\\ \therefore y=3x+6\left\{given\text{equation}\right\}\\ \therefore m=3\end{array}$

Now, from option,

  $\begin{array}{l}x-\frac{1}{3}y=0\\ \therefore y=3x\\ \because y=mx+c\left\{\text{equation of a line}\right\}\\ \therefore m=3\end{array}$

Therefore, the equation $x-\frac{1}{3}y=0$ represents a line parallel to the given graph of $y=3x+6$

Hence, the correct option is (F).