Question

Daphne has a preloaded games card that she is using to play games at the arcade as shown in the table.

Answer 1

(a) Daphne starts with $25.00 on her card

(b) The amount by which her card value changes per game is -($0.5)

(c) y = 25 - 0.5·x

From the table of values, the amount

The table of values is presented as follows;

$\begin{array}{ccc}&\ \ Games \ Played#&Amount \ on \ Card \ (\ )\\Start&0&25\\&3&23.5\\&6&22\\&9&20.50\end{array}$

(a) From the table above, when the number of game played = 0, the amount on the card = 25

Therefore;

The amount that Daphne start with on her card = $25

(b) The amount her card changes per game is given by the rate of change as follows;

$Rate \ of \ change = \dfrac{dy}{dx}$

Therefore;

$Rate \ of \ change = \dfrac{y_2 - y_1}{x_2 - x_1}$

Which gives;$Rate \ of \ change = \dfrac{Present \ amount \ on \ card - Previous \ amount \ on \ card}{Present \ number of games played - Previous\ number of games played}$Taking any two points, we get;

Rate of change = (23.5 - 25)/(3 - 0) = -0.5

Therefore, her card value is drops by 0.5 per game

The amount by which her card value changes per game = -($0.5)

(c) We note that the rate of change of the Amount on Card, y, to the

number of Games Played, x, is constant, therefore, the relationship

between the variables is a straight line relationship, of the form, y = m·x + c, and we have;

m = The rate of change = -0.5

c = The y-intercept = The starting Amount on Card ($) = 25

Therefore, the equation is;

y = -0.5·x + 25 = 25 - 0.5·x

The required equation is, y = 25 - 0.5·x

Where;

y = The Amount on Card

x = The number of Games Played

Learn more about straight line equations here;

brainly.com/question/16934180