(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;
[tex]\begin{array}{ccc}&\ \ Games \ Played#&Amount \ on \ Card \ (\$)\\Start&0&25\\&3&23.5\\&6&22\\&9&20.50\end{array}[/tex]
(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;
[tex]Rate \ of \ change = \dfrac{dy}{dx}[/tex]
Therefore;
[tex]Rate \ of \ change = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Which gives;[tex]Rate \ of \ change = \dfrac{Present \ amount \ on \ card - Previous \ amount \ on \ card}{Present \ number of games played - Previous\ number of games played}[/tex]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;
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