Question

a dance school offers classes in ballet folklórico. there is a one - time registration fee and an additional charge for each class. the total cost of classes, y, is a linear function of the number of classes taken, x. three classes cost $36. seven classes cost $68. points on the graph: (3, 36) and (7, 68) rate of change: 8 y = 8x + b which ordered pair would you like to use to find the initial value? (3, 36) (7, 68)

Explanation:

To find the initial value \( b \) in the linear equation \( y = 8x + b \), we can use either ordered pair since the equation is linear and holds for all points on the line. Both \((3, 36)\) and \((7, 68)\) are valid points on the graph of the linear function, so either can be substituted into the equation \( y = 8x + b \) to solve for \( b \). For example, using \((3, 36)\): substitute \( x = 3 \) and \( y = 36 \) into \( y = 8x + b \), we get \( 36 = 8(3) + b \), which can be solved for \( b \). Similarly, using \((7, 68)\): \( 68 = 8(7) + b \) also works. However, since the question asks which one to use, either is correct, but let's pick one (e.g., \((3, 36)\) for simplicity).

Answer:

\((3, 36)\) (or \((7, 68)\) as both are valid; here we choose \((3, 36)\))