this question hurts my brain

Question

dylan walks into a video arcade with a pocket full of quarters. He spends them at a rate of nine every half hour until he runs out. If the amount of quarters Dylan has is graphed overtime, which feature of the graph corresponds to Dylan‘s initial amount of quarters, Before he spends the first one?

a. y intercept

b. slope

c. x intercept

d. minimum value

Answer 1

Hello, Rachel,

Dylan is spending at a constant rate of 9 quarters per half hour. I'll make this a rate of 18 per hour, for convenience. Since the rate is constant, his spending behavior can be expressed as a linear equation of the form

y = mx + b

where y is the number of quarters, m is the slope (in this case the rate of spending), x is time (I'll make it 1 hour increments), and b is the y intercept at x = 0. Since Dylan's quarter stash drops with time, the slope here would be -18 quarters/hour.

y = -18x + b

At x = 0, the time Dylan arrived at the machine with a big grin, he had b quarters since y = -18*0 + b, or y = b.

Say that Dylan came with 100 quarters, for example. That 100 would be the point at which the line crosses the y axis at t = 0, or (0,100). So Dylan's initial quarter count is the y intercept.

Bob