Identify the slope. Remember slope is a ratio.
y ={2}{3}x + 8

9514 1404 393

  2/3

Step-by-step explanation:

Assuming your equation is supposed to be ...

 

the slope is the coefficient of x.

The slope is 2/3.

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.