Chapter 1.1, Problem 103E

To determine

Draw the equation of the line which is of the form of $\frac{x}{a}+\frac{y}{b}=1$ .Also use the graph to make a conjecture about what a and b represent , verify.

Explanation of Solution

Given: It is given in the question that the equation is $\frac{x}{\frac{1}{2}}+\frac{y}{5}=1$ .

Graph:

  

Interpretation: First ,it is need to get rid of the denominator and to do that,multiply the denominator of one term to both sides of rhe equation .

  $\begin{array}{l}\frac{x}{\frac{1}{2}}+\frac{y}{5}=1\\ \frac{2x}{1}+\frac{y}{(5)}=1\end{array}$

  $5(\frac{2x}{1})+(5)(\frac{y}{5})=1\times 5$

Then,multiply the other denominator to both sides ,

  $10x+y=5$

Next,arrange the equation into y − intersept form,

  $y=-10x+5$

In this equation ,it would see that $-10$ and $1$ are actually x and y intercepts.