Chapter 2, Problem 18STP

Interpretation Introduction

Interpretation:

The slope of the line should be determined.

Concept introduction:

The slope of a line determines the direction of the line. To slope can be determined by dividing the difference of the 2 points of y-coordinate by the difference of the 2 the points of x-coordinates of those same 2 points. The formula for the slope is error is as follows:

$\text{Slope = }\frac{y_{\text{2}}-y_{\text{1}}}{x_{\text{2}}-x_{\text{1}}}$

Answer to Problem 18STP

Option (D) 7.5 y/m.

Explanation of Solution

The value of the slope can be calculated using the point A and B shown in the image:

$\begin{array}{l}\text{Slope = }\frac{y_{\text{B}}-y_{\text{A}}}{x_{\text{B}}-x_{\text{A}}}\\ \text{Slope = }\frac{\left(575-500\right)\text{y}}{\left(90-80\right)\text{m}}\\ \text{Slope = }\frac{75\text{ y}}{10\text{ m}}\\ \text{Slope = }7.5\text{ y}/\text{m}\end{array}$

Hence, the correct answer is Option (D).

Conclusion

Option (A) 0.00 m/y. The slope 0 is observed when the line is horizontal, here the line is not horizontal, hence, it is an incorrect answer.

Option (B) 0.13 m/y. As the formula of the slope has the value of y axis as numerator and x as denominator, the value of the slope will always be represented as y/m, not m/y. Hence, it is an incorrect answer.

Option (C) 0.13 y/m. According to the calculations, the value of slope is 7.5 y/m. Hence, it is an incorrect answer.

Option (E) 7.5 m/y. Here, the value of slope is correct, but as the y axis represents the age of ice and x axis represents the depth, the value should have unit y/m. Hence, it is an incorrect answer.