Question

Renata wins a $20 gift card to an online music site. After Renata purchases 16 songs, the gift card has a remaining balance of $0. Which equation represents the relationship between y, the remaining balance on Renata’s gift card, and x, the number of songs purchased?

Answer 1

Answer:

5x + 4y = 80

Step-by-step explanation:

Answer 2

Answer:

5x + 4y = 80

Step-by-step explanation:

First, let us look at the given:

x = The number of songs purchased

y = The remaining balance of Renata's gift card

Coordinates:

1. (16,0)

2. (0,20)

                                                                                   

Now let's look at the unknown:

Slope = ?

Since we have the coordinates we can easily apply the slope formula

$slope = \frac{y2 - y1}{x2 - x1}$

$slope = \frac{20 - 0}{0 - 16} = \frac{20}{-16}$

Now that we have our slope we can use either point-slope formation or slope-intercept formation, just pick whichever one you're comfortable with.

                                                                                                           

Point-slope formation

y - y1 = slope (x - x1)

Now just plug in the numbers:

y - 0 = 20/-16 (x - 16)

Now you multiply both sides by -16 to get rid of the fraction

-16(y - 0) = -16 (20/-16) (x - 16)

-16y - 0 = 20 (x - 16)

-16y = 20x - 320

Now subtract 20 from both sides.

-16y - 20x = 20x - 20x - 320

-20x - 16y = -320

Now we need to simplify both sides so we divide both sides by 4

$\frac{-20x - 16y = -320}{4}$

-5x - 4y = -80

Now, remember, one of the rules of standard formation is that the coefficient of x cannot be smaller than zero. So you need to multiply both sides by -1.

-1 (-5x - 4y) = (-80) -1

5x + 4y = 80

But this is all assuming yall are on Edgenuity lol