Question

climbing indra 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 indras height to the number of hours she is mountain climbing.

time (hours) x 0 2 4 5
height (meters) y 182.5 109.5 36.5 0

a. find the intercepts
the x - intercept is
the y - intercept is
b. describe what the intercepts mean in the context of the situation

Explanation:

Step1: Recall intercept - definition

The x - intercept is the value of x when y = 0, and the y - intercept is the value of y when x = 0.

Step2: Find the y - intercept

From the table, when x = 0, y = 182.5. So the y - intercept is 182.5.

Step3: Find the x - intercept

We know that the relationship is linear. The rate of change (slope) m=-36.5 (since she descends 36.5 meters per hour). The equation of the line in slope - intercept form is y = mx + b, where m=-36.5 and b = 182.5. Set y = 0:
0=-36.5x + 182.5
36.5x=182.5
x = 5

Answer:

a. The x - intercept is 5 and the y - intercept is 182.5.
b. The y - intercept (182.5) represents Indra's starting height above sea - level (182.5 meters) at the start of the day (x = 0 hours). The x - intercept (5) represents the number of hours it takes for Indra to reach sea - level (y = 0 meters) as she descends at a rate of 36.5 meters per hour.