Chapter 1.3, Problem 11CFU

a.

To determine

To find: two ordered pairs that represent the function

Answer to Problem 11CFU

  $\left(38.5000,173\right)\text{ and }\left(44.125,188\right)$

Explanation of Solution

Given information:

Length of first tibia, $\left(tibi{a}_1\right)=38.500\text{ cm}$

Height of first tibia, $\left(h_1\right)=173\text{ cm}$

Length of second tibia, $\left(tibi{a}_2\right)=44.125\text{ cm}$

Height of second tibia, $\left(h_2\right)=188\text{ cm}$

Calculation:

The two ordered pair for first and second tibia will be as follows:

  $\left(tibi{a}_1,h_1\right)\text{ and }\left(tibi{a}_2,h_2\right)$

Put the values of the tibias to get the ordered pairs as follows:

  $\left(38.500\text{ cm},173\text{ cm}\right)\text{ and }\left(\text{44}\text{.125 cm, }188\text{ cm}\right)$

b.

To determine

slope of line through the two points.

Answer to Problem 11CFU

  $\frac{8}{3}$

Explanation of Solution

Given information:

Length of first tibia, $\left(tibi{a}_1\right)=38.500\text{ cm}$

Height of first tibia, $\left(h_1\right)=173\text{ cm}$

Length of second tibia, $\left(tibi{a}_2\right)=44.125\text{ cm}$

Height of second tibia, $\left(h_2\right)=188\text{ cm}$

The ordered pairs is $\left(38.500\text{ cm},173\text{ cm}\right)\text{ and }\left(\text{44}\text{.125 cm, }188\text{ cm}\right)$

Calculation:

The slope formula is as follows:

  $m=\frac{y_2-y_1}{x_2-x_1}$

Put the values in the slope formula and simplify it as shown below.

  $\begin{array}{c}m=\frac{188\text{ cm}-173\text{ cm}}{\text{44}\text{.125 cm}-38.500\text{ cm}}\\ =\frac{15}{5.625}\\ =\frac{8}{3}\end{array}$

Thus, the slope value is $\frac{8}{3}$ .

c.

To determine

To explain: the meaning of slope in this context.

Answer to Problem 11CFU

The slope for this linear line equation is positive. As the length of tibia person increases, their height also increases. The increase in height of a tibia is $\frac{3}{8}$ the increase in length of the tibia.

Explanation of Solution

Given information:

Length of first tibia, $\left(tibi{a}_1\right)=38.500\text{ cm}$

Height of first tibia, $\left(h_1\right)=173\text{ cm}$

Length of second tibia, $\left(tibi{a}_2\right)=44.125\text{ cm}$

Height of second tibia, $\left(h_2\right)=188\text{ cm}$

Calculation:

The ordered pairs is $\left(38.500\text{ cm},173\text{ cm}\right)\text{ and }\left(\text{44}\text{.125 cm, }188\text{ cm}\right)$

Slope of these two point, m = $\frac{8}{3}$

The slope intercept formula is as follows:

  $y=mx+b$

The above formula can be rewritten after ignoring b as follows:

  $height=\left(\frac{8}{3}\right)\left(tibia\right)$

Here height is y, tibia is x and slope is$\frac{8}{3}$ .

The slope for this linear line equation is positive, as the length of tibia person increases, their height also increases. If their height increases by three, their length increases by 8. The increase in height of a tibia is $\frac{3}{8}$ the increase in length of the tibia.

So, for 1 cm growth of tibia, their height becomes $\frac{3}{8}$ cm.