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Question 936874: I would really appreciate your help in the following question.
Lora has a gift card where all downloads for music cost the same amount. after downloading 2 songs, the balance on her card was $18.10. after downloading a total of 5 songs, the balance was $15.25
1. write an equation in slope-intercept form that represents the amount in dollars remaining on the card as a function of songs downloaded.
2. identify the slope of the line and tell what the slope represents.
3.identify the y intercept of the line and tell what it represents.
4. how many additional songs can Lora download when there is $15.25 left on the card?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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:
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