Chapter 5.5, Problem 28P

For each graph, find the $x$- and $y$-intercepts. Then write an equation in standard form using integers.

To determine

To find:. The equation of the line in the below graph:

  

Answer to Problem 28P

From the given graph,

x -intercept: $a=3$

y -intercept: $b=-2$

The standard form of the given equation is $2x-3y=6$ .

Explanation of Solution

Given information:

The given graph is

  

From the given graph,

x -intercept: $a=3$

y -intercept: $b=-2$

So the equation in intercepts form is

  $\begin{array}{l}\frac{x}{a}+\frac{y}{b}=1\\ \Rightarrow \frac{x}{3}+\frac{y}{-2}=1\end{array}$

Now, rewriting the equation in standard form as follows:

  $\begin{array}{l}\frac{x}{3}+\frac{y}{-2}=1\\ \Rightarrow \frac{x}{3}-\frac{y}{2}=1\\ \Rightarrow 2x-3y=6\end{array}$

Conclusion:

Therefore, the standard form of the given equation is $2x-3y=6$ .