Question

You're backpacking up Mount impossible and started at a elevation of 500 fee. Two hours later you climbed another 600 feet and you're at a total of 1100 ft, and after hiking 9 hours in all your at a elavation of 3200 ft.

1.What is the slope?
2.What is the y intercept?

Answer 1

The slope of the path up Mount Impossible is 300 feet per hour, and the y-intercept, which represents the starting elevation, is 500 feet.

Step-by-step explanation:

To determine the slope and y-intercept from the situation described, we must consider the elevation changes as the 'rise' and the time passed as the 'run' when using the slope formula (slope = rise/run). Initially, the hiker starts at 500 feet and after 2 hours is at 1100 feet, resulting in a rise of 600 feet. The slope can thus be calculated with a rise of 600 feet over a run of 2 hours, giving us a slope of 300 feet per hour. At the end of 9 hours, the hiker is at 3200 feet. This information can be used to derive an equation representing the elevation (y) after a certain number of hours (x). If we assume a linear relationship, the equation would be of the form y = mx + b, where 'm' is the slope, and 'b' is the y-intercept.

To find the y-intercept, we can plug in the values we know from any point on this line. Taking the starting point, we know that at x=0 hours, the elevation y is 500 feet. Thus, the y-intercept is 500 feet, meaning the equation becomes y = 300x + 500.