Chapter B, Problem 25E

To determine

To calculate: To find the slope and y-intercept of the line and then draw its graph

Answer to Problem 25E

Slope of line is $-\frac{1}{3}$ and y-intercept of line is $0$

Explanation of Solution

Given information: Equation is $x+3y=0$

Formula Used:

Slope intercept form of line is

  $y=mx+c$

Where,

  $m=$ Slope

  $c=$ y-intercept

Calculation:

Equation of line is given as follows:

  $x+3y=0$

Rewriting the equation as follows:

  $\begin{array}{l}3y=-x\\ y=-\frac{1}{3}x+0\end{array}$

Comparing the above equation with slope-intercept form of line $y=mx+c$ ,

  $\begin{array}{l}m=-\frac{1}{3}\\ c=0\end{array}$

Finding the points that lie on equation:

When $x=0$

  $\begin{array}{l}y=-\frac{1}{3}\left(0\right)\\ y=0\end{array}$

When $x=3$

  $\begin{array}{l}y=-\frac{1}{3}\left(3\right)\\ y=-1\end{array}$

When $x=6$

  $\begin{array}{l}y=-\frac{1}{3}\left(6\right)\\ y=-2\end{array}$

Thus, $\left(0,0\right),\left(3,-1\right),\left(6,-2\right)$ are the solution of equation and must lie on the equation.

Plotting the points on graph,

  y-axis

    x-axis

Conclusion:

Hence, slope of line is $-\frac{1}{3}$ and y-intercept of line is $0$