A leatherback sea turtles was swimming at 850 below sea level. He went 165 meters and then descendes 165 meters. Draw a number line to show the change in position of the sea turtles from depth it was swimming. What integer represents the sea turtles change in position?

The answer is below

Step-by-step explanation:

a) Let negative means the turtle position when descending and positive for going up. Therefore since the turtle was 850 meters below see level, it was at -850. It then moves 165 meters up, hence its new position is -685 meters (-850 + 165). Lastly it moves down 165 meters, hence its new position is -850 meters (-685 - 165)

b) The change in position is the sum of the movements = +165 - 165 = 0 meters.

A) The rate of change is -30, and it represents the number of songs taken off of her download list each week.
The initial value is 150, and it represents the number of songs she wants to download to begin with.

B) y = -30x + 150

Explanation
A) The rate of change can be found by using the slope formula between the first two points, (0, 150) and (1, 120):
m=(y₂-y₁)/(x₂-x₁) = (120-150)/(1-0) = -30/1 = -30

The initial value is the y-value of the first point on the graph, (0, 150).

B) The equation is in slope-intercept form, y=mx+b, where m represents the slope and b represents the y-intercept.  The slope is the rate of change that we found in part A; the y-intercept is the initial value we found in part A.  This gives us the equation y=-30x+150.