Ivy has borrowed 150 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: 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. part b: write an equation in slope-intercept form to model the relationship between x and y.

A) rate of change would be dividing the number of songs wanted (150) by the number of weeks downloading (5)

150/5 = 30

 since the total quantity wanted is becoming less every week the rate of change would be negative so it becomes -30

Initial value is 150, which is the total number of songs they want

B)

 to write an equation find 2 points on the graph the line passes through:

lets use p1(0, 150), p2(1, 120)
calculate the slope:
m = (y2- y1)/(x2 - x1) = (120 - 150)/(1 - 0)
m = -30
and now use line equation in form point-slope:
y - y1 = m(x - x1)
y - 150 = -30(x - 0)
y = -30x + 150

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.