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Please help me understand this. Thank you! Gina has borrowed 100 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x: A graph titled Song Downloading shows the Number of Weeks on x-axis and Number of Songs Left to Download on the y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 140 at increments of 20. A straight line joins the ordered pairs 0, 100 and 1, 80 and 2, 60 and 3, 40 and 4, 20 and 5, 0. Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points) Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)

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Answer:

Rate of Change/Slope = -20

Equation: y= -20x +100

Step-by-step explanation:

A. We know the rate of change is also known as the slope.  If we used the slope formula to find the slope we can find the Rate of Change.

[tex]\frac{y2 - y1}{x2 - x1} = \frac{100-80}{1-2} = \frac{20}{-1} = -20[/tex]

B. Since we know the slope and 1 point on the graph we can substitute them in for 'b'

(0,100)

(100)=-20(0) + b

b = 100

Since we know the slope and the b value we can write the equation:\

y = -20x +100

fichoh

The rate of change refers to the slope of the line, that is the change in y-axis per unit change in the value on the x-axis. Hence, the rate of change is :

  • Slope = - 20
  • y = -20x + 100

  • Slope = Rise / Run

  • Rise = (y2 - y1) = (0 - 100) = - 100

  • Run = (x2 - x1) = (5 - 0) = 5

Slope = - 100 / 5 = - 20

General form of a slope - intercept relation :

  • y = bx + c

The intercept, c can be calculated thus:

100 = - 20(0) + c

100 = 0 + c

c = 100

Hence, the slope - intercept equation will be y = - 20x + 100

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