Question 936874
let x = number of songs that are downloaded.


when x = 2, the remaining balance is 18.10


when x = 5, the remaining balance is 15.25


the slope intercept form of the equation for a straight line is y = mx + b


m is the slope
b is the y-intercept.


the formula for the slope is:


m = (y2 - y1) / (x2 - x1)


(x1,y1) = (2,18.10)
(x2,y2) = (5,15.25)


the x-value of the coordinate pair is the number of songs that were downloaded.
the y-value of the coordinate pair is the remaining balance.


slope = m = (y2-y1) / (x2-x1) = (15.25 - 18.10) / (5 - 2) = -2.85 / 3 = -.95


replace m with -.95 in the slope intercept form of the equation to get:


y = -.95 * x + b


now you want to solve for b, which is the y-intercept.


take any one of the point pairs on the line and replace y with the y-coordinate and replace x with the x-coordinate and solve for b.


we'll use the point (2,18.1)


y = -.95 * x + b becomes:


18.1 = -.95 * 2 + b


simplify to get:


18.1 = -1.9 + b


add 1.9 to both sides of the equation to get:


18.1 + 1.9 = -1.9 + 1.9 + b


combine like terms to get:


20 = b


that's your y-intercept.


the slope intercept form of the equation becomes:


y = -.95 * x + 20


answer to question 1:


the equation is y = -.95 * x + 20


answer to question 2:


the y-intercept is 20.


it represents the remaining balance of the account before any songs were downloaded.


answer to question 3:


find out the x-intercept.


the x-intercept is the value of x when y is equal to 0.


this will be when there is no more money remaining in the account.


find this by setting y = 0 and solving for x.


equation of y = -.95 * x + 20 becomes:


0 = -.95 * x + 20


subtract 20 from both sides of this equation to get:


-20 = -.95 * x + 20 - 20


combine like terms to get:


-20 = -.95 * x


divide both sides of this equation by -.95 to get:


-20 / -.95 = x


solve for x to get:


x = 21.0505263158 which we can rounded off to 21.05.


when she bought 21 cd, she had a small balance left.


that balance is y = -.95 * 21 + 20 = .05 dollars which is equal to 5 cents.


there's not enough money left in the account to buy another song, so this is her limit.


when she had 15.25 remaining balance, she had already bought 5 songs.


she will run out of money when she buys 21 songs.


she can buy an additional 21 - 5 = 16 songs before she runs out of money.


this can all be represented on the graph, which is shown below:


<img src = "http://theo.x10hosting.com/2015/010701.jpg" </>