Question

emma is mountain climbing and starts the day at 182.5 meters above sea level. each hour she descends 36.5 meters. the table shows the function relating emmas height to the number of hours she is mountain climbing. find the intercepts and describe what they mean in the context of the situation.
the x - intercept is __ and it means __.
the y - intercept is __ and it means __.
sketch a graph with a y - intercept of 4 and x - intercepts of - 3 and 8.

Explanation:

Step1: Find the y - intercept

The y - intercept occurs when \(x = 0\). From the table, when \(x=0\), \(y = 182.5\). In the context of the problem, this means that at the start of her climbing (when \(x = 0\) hours), Emma's height above sea level is \(182.5\) meters.

Step2: Find the x - intercept

The x - intercept occurs when \(y = 0\). From the table, when \(y = 0\), \(x=5\). In the context of the problem, this means that after \(5\) hours of climbing, Emma reaches sea level (\(y = 0\) meters).

Answer:

The y - intercept is \(182.5\) and it means Emma's initial height (at \(x = 0\) hours) is \(182.5\) meters. The x - intercept is \(5\) and it means after \(5\) hours of climbing, Emma reaches sea level (\(y=0\) meters).