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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?
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## 1 Answer

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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 $y=m x+b$
$m$ is the slope
$b$ is the $y$-intercept.
the formula for the slope is:
\begin{aligned} &m=(y 2-y 1) /(x 2-x 1) \\ &(x 1, y 1)=(2,18.10) \\ &\left(x^{2}, y^{2}\right)=(5,15.25) \end{aligned}
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 $=m=(y 2-y 1) /(x 2-x 1)=(15.25-18.10) /(5-2)=-2.85 / 3=-.95$
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 $21 \mathrm{~cd}$, 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.
by Platinum (91,198 points)

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