Question

A geologist measure the temperature T (in ${}^{\circ }C$) of the soil at various depths below the surface and finds that at a depth of x cm, the temperature is given by given by width="94" height="20" role="math">T=0.08x-4.

(a) What is the temperature at a depth of 1 m (100 cm)?

(b) Sketch a graph of linear equation.

(c) What do the slope, the x-intercept, and T-intercept of the graph represent?

Short answer

(a) $T=4^{o}C$

(b) The graph of linear equation is

(c) Here, the x-intercept represent the soil depth and, the T-intercept represent that the soil temperature was$-4{(}^{o}C)$ at the time of starting temperature.

Step-by-step solution

Part a. Step 1. Determination of abscissa and ordinate.

Here x represent the abscissa and T represent the ordinate.

Part a. Step 2. Given equation.

The equation is

$T=0.08x-4$

where T is in ${(}^{o}C)$and x is in (cm).

Part a. Step 3. Determining the temperature.

When $x=1m$

$=100cm$

$T=0.08\times 100-4$

$$\begin{gathered} =8-4 \\ =4C^{\circ } \end{gathered}$$

Part b. Step 1. Determination of abscissa and ordinate.

Here x represent the abscissa and T represent the ordinate.

Part b. Step 2. Determination of some points to plot graph.

x	T
0	$-4$
1	$-3.92$
$-1$	$-4.08-4$

Part b. Step 3. Plotting the graph.

Part c. Step 1. Slope Represent.

Here, $T=0.08x-4$

So, the slope represents an increase of 0.08${(}^{o}C)$ in temperature of the soil as the depth increase.

Part c. Step 2. T-intercept represent.

Here, the T-intercept represent that the soil temperature was$-4{(}^{o}C)$ at the time of starting temperature.

Part c. Step 3. X-intercept represent.

Here, the x-intercept represent the soil depth was 50 cm at the time of starting temperature.