Final answer:
The equation in point-slope form representing Guy's card balance is y = -7x + (7*8 + 5), where x represents the number of games he buys, and y represents his card balance.
Step-by-step explanation:
The equation in point-slope form representing Guy's card balance is y = -7x + (7*8 + 5), where x represents the number of games he buys, and y represents his card balance. In this equation, the coefficient of x is -7, which represents the slope of the line.
The negative value of the slope indicates that as the number of games he buys increases, his card balance decreases. The y-intercept, which is determined by the constant term in the equation, represents Guy's initial card balance without buying any games.
For example, if Guy buys 3 games, we can substitute x = 3 into the equation to find the corresponding y value:
y = -7(3) + (7*8 + 5)
y = -21 + 56 + 5
y = 40