Chapter 3.2, Problem 29OE

To determine

To find: The coordinates of the points where given line crosses the coordinate axes.

Answer to Problem 29OE

The line crosses the coordinate axes at the points $(2,0)and(0,3)$ .

Explanation of Solution

Given information: Given equation of line is $\frac{x}{2}+\frac{y}{3}=1$ .

Calculation:

When line crosses $x-axis$ , then $y=0$ .

So putting $y=0$ in given equation,

  $\begin{array}{l}\frac{x}{2}+\frac{0}{3}=1\\ \Rightarrow \frac{x}{2}=1\\ \Rightarrow x=2\end{array}$

So, the given line crosses the $x-axis$ at the point $(2,0)$ .

When line crosses $y-axis$ , then $x=0$ .

So putting $x=0$ in given equation,

  $\begin{array}{l}\frac{0}{2}+\frac{y}{3}=1\\ \Rightarrow \frac{y}{3}=1\\ \Rightarrow y=3\end{array}$

So, the given line crosses the $y-axis$ at the point $(0,3)$ .

Thus, the line crosses the coordinate axes at the points $(2,0)and(0,3)$ .