Chapter 4.2, Problem 53STP

To determine

To Find:

Best equation represents the graph.

Answer to Problem 53STP

  $y=-\frac{1}{2}x$

Explanation of Solution

Given Graph:

  

Concept Used:

Equation of slope-intercept form of a line is given by:

  $\begin{array}{l}y=mx+b\mathrm{............................}(1)\\ where\\ b=y-intercept\\ m=\frac{raise}{run}=slope\end{array}$

Calculation:

We can interpret from the graph that from (0,0), we go down 1 unit and then go right 2 units , then we reach at point (2,-1)

So, $slope=\frac{rise}{run}=-\frac{1}{2}$

And since the line passes through (0,0), y-intercept is 0

Hence,

  $\begin{array}{l}m=-\frac{1}{2}\\ b=0\end{array}$

  

WRITING THE EQUATION OF LINE :

  $\begin{array}{l}y=mx+b\mathrm{................................}[slope-\mathrm{int}ercept]\\ y=-\frac{1}{2}x+\mathrm{0............................}[m=-\frac{1}{2},b=0]\\ \Rightarrow y=-\frac{1}{2}x\end{array}$

So, the required equation is given by:

  $\begin{array}{l}y=-\frac{1}{2}x\\ \end{array}$