Question

question 2: determine which representation – table of values, graph, or equation – you would rather use to find the y-intercept of the function that represents the total cost of a cell phone plan with an enrollment fee and a monthly fee after a certain number of months. justify your choice.

Explanation:

To find the \( y \)-intercept (initial cost, which is the enrollment fee here) of the function representing the total cost of the cell phone plan, using an equation is efficient. The total cost function for the plan can be modeled as a linear function \( y = mx + b \), where \( y \) is the total cost, \( x \) is the number of months, \( m \) is the monthly fee (slope), and \( b \) is the \( y \)-intercept (enrollment fee). By identifying the equation from the plan details (monthly fee as \( m \) and enrollment fee as \( b \)), we can directly read the \( y \)-intercept as \( b \). Using a table would require finding when \( x = 0 \) (no months, just enrollment), but if the table doesn't have \( x = 0 \), we'd need to extrapolate. For a graph, we'd have to find where the line crosses the \( y \)-axis (when \( x = 0 \)), but reading the exact value from a graph can be less precise, especially if it's not scaled or labeled clearly. The equation gives a direct, precise value for the \( y \)-intercept (enrollment fee) without needing to extrapolate or estimate from a graph/table.

Answer:

I would rather use an equation to find the \( y \)-intercept. The total cost function for the cell phone plan is linear (\( y = mx + b \), where \( m \) is the monthly fee, \( x \) is months, \( b \) is the \( y \)-intercept/enrollment fee). The equation directly gives \( b \) (enrollment fee) as the \( y \)-intercept. A table may lack \( x = 0 \) (requiring extrapolation), and a graph may have estimation errors, but the equation provides the exact \( y \)-intercept without such issues.