The standard form of the equation that represents the number of quarters, q, and the number of dimes, d, that Austin has in his piggy bank is 5q + 2d = 270. Explain what the intercepts mean in terms of the context and how to find them.

Answer:

To find the q-intercept, set d = 0 and solve: 5q = 270, so q = 54. This means Austin could have 54 quarters and 0 dimes. To find the d-intercept, set q = 0 and solve: 2d = 270, so d = 135. This means Austin could have 135 dimes and 0 quarters. The intercepts represent the maximum amount of one type of coin Austin could have if he has none of the other type.