Question

Imagine you're climbing a mountain. During the first 4 miles, you go up 1000 feet per hour or 4000 feet total. For the next 2 miles, the mountain is less steep, and you ascend 500 feet per hour, or 1000 feet total. The last mile, you ascend 300 feet and reach the top. What is the independent variable, dependent variable, and graph for an equation?

A. Independent variable: Distance in miles, Dependent variable: Elevation in feet, Graph: Elevation vs. Distance
B. Independent variable: Time in hours, Dependent variable: Distance in miles, Graph: Distance vs. Time
C. Independent variable: Elevation in feet, Dependent variable: Time in hours, Graph: Time vs. Elevation
D. Independent variable: Distance in miles, Dependent variable: Time in hours, Graph: Time vs. Distance

Answer 1

The independent variable in climbing a mountain is the distance in miles, and the dependent variable is the elevation in feet, making the graph an Elevation vs. Distance graph.

Step-by-step explanation:

In the scenario where a student is climbing a mountain, the independent variable is the distance in miles because this is the variable that is controlled or manipulated by the climber. The dependent variable is the elevation in feet because it changes in response to the distance climbed. Consequently, the correct answer is: A. Independent variable: Distance in miles, Dependent variable: Elevation in feet, Graph: Elevation vs. Distance. When graphing this relationship, the distance will be placed on the horizontal axis (x-axis), and the elevation on the vertical axis (y-axis). Given a linear relationship, this would typically be represented by the equation of a straight line which can be written in the form y = mx + b. Here, 'm' would represent the slope, or rate of ascent (elevation gain per unit of distance), and 'b' would represent the y-intercept, or the elevation at the beginning of the climb (which could be zero if starting at sea level or another known elevation).