Chapter 1.3, Problem 26E

a.

To determine

To find: The slope of line .

Answer to Problem 26E

The slope of line is $=\frac{-5}{4}$ .

Explanation of Solution

Given Information: Given a graph which shows the amount of money.

Calculation:

The slope of line $=\frac{y_2-y_1}{x_2-x_1}$

  $=\frac{0-30}{24-0}$

  $=\frac{-30}{24}=\frac{-5}{4}$

b.

To determine

To find:The domain and range of function.

Answer to Problem 26E

Domain (0,24), Range (0,30).

Explanation of Solution

Given Information: - Given a graph which shows the amount of money.

Calculation:

The slope of line $=\frac{y_2-y_1}{x_2-x_1}$

  $=\frac{0-30}{24-0}$

  $=\frac{-30}{24}=\frac{-5}{4}$

This shows loan balance will decrease in 2 years linearly

The domain of the function is (0,24).

The range of the function is (0,30) domain represents time lie between 0 and 24 months and range represent balance of loan lie between 0 and 30.

c.

To determine

To find :Money owe after making payments for 12 months.

Answer to Problem 26E

After 12 months the owe is $15$ dollars.

Explanation of Solution

The slope of line $=\frac{y_2-y_1}{x_2-x_1}$

  $=\frac{0-30}{24-0}$

  $=\frac{-30}{24}=\frac{-5}{4}$

This shows loan balance will decrease in 2 years linearly

The domain of the function is (0,24).

The range of the function is (0,30) domain represents time lie between 0 and 24 months and range represent balance of loan lie between 0 and 30.

Equationof lineis

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-30=\frac{-5}{4}(x-0)\end{array}$

  $\begin{array}{l}y-30=\frac{-5}{4}x\\ y=\frac{-5}{4}x+30\end{array}$

After 12 months the value of

  $\begin{array}{l}y=\frac{-5}{4}\times 12+30\\ y=-15+30\\ y=15\end{array}$

Thus, After 12 months the loan balance is $15$ dollars.