Chapter 1.1, Problem 40E

(a)

To determine

To explain: The reason for $c$ and $d$ are the x -intercept and y -intercept of the equation of given line respectively.

Answer to Problem 40E

The value of x for $y=0$ is $x=c$ , so it is the x -intercept and the value of y for $x=0$ is $y=d$ , so it is the y -intercept.

Explanation of Solution

Given information: The equation is $\frac{x}{c}+\frac{y}{d}=1$ .

Calculation:

Substitute $0$ for $x$ in the equation $\frac{x}{c}+\frac{y}{d}=1$ .

  $\begin{array}{c}\frac{0}{c}+\frac{y}{d}=1\\ \frac{y}{d}=1\\ y=d\end{array}$

Substitute $0$ for $y$ in the equation $\frac{x}{c}+\frac{y}{d}=1$ .

  $\begin{array}{c}\frac{x}{c}+\frac{0}{d}=1\\ \frac{x}{c}=1\\ x=c\end{array}$

Therefore, the value of x for $y=0$ is $x=c$ , so it is the x -intercept and the value of y for $x=0$ is $y=d$ , so it is the y -intercept.

(b)

To determine

To explain: The relation between x -intercept and y -intercept with $c$ and $d$ .

Answer to Problem 40E

The x -intercept is $2c$ and y -intercept is $2d$ .

Explanation of Solution

Given information: The equation is $\frac{x}{c}+\frac{y}{d}=2$ .

Calculation:

Substitute $0$ for $x$ in the equation $\frac{x}{c}+\frac{y}{d}=2$ .

  $\begin{array}{c}\frac{0}{c}+\frac{y}{d}=2\\ \frac{y}{d}=2\\ y=2d\end{array}$

Substitute $0$ for $y$ in the equation $\frac{x}{c}+\frac{y}{d}=2$ .

  $\begin{array}{c}\frac{x}{c}+\frac{0}{d}=2\\ \frac{x}{c}=2\\ x=2c\end{array}$

Therefore, the x -intercept is $2c$ and y -intercept is $2d$ .