For each situation, (a) write an equation in the form y=m...

For each situation, (a) write an equation in the form $y=m x+b,(b)$ find and interpret the ordered pair associated with the equation for $x=5,$ and $(c)$ answer the question. A cell phone plan includes 900 anytime minutes for $\$ 60$ per month, plus a one-time activation fee of $\$ 36 . \mathrm{A}$ Nokia 6650 cell phone is included at no additional charge. (Source: AT\&T.) Let $x$ represent the number of months of service and $y$ represent the cost. If you sign a 1-yr contract, how much will this cell phone plan cost? (Assume that you never use more than the allotted number of minutes.)

For each situation, (a) write an equation in the form $y=m x+b,(b)$ find and interpret the ordered pair associated with the equation for $x=5,$ and $(c)$ answer the question.
A cell phone plan includes 900 anytime minutes for $\$ 60$ per month, plus a one-time activation fee of $\$ 36 . \mathrm{A}$ Nokia 6650 cell phone is included at no additional charge. (Source: AT\&T.) Let $x$ represent the number of months of service and $y$ represent the cost. If you sign a 1-yr contract, how much will this cell phone plan cost? (Assume that you never use more than the allotted number of minutes.)

Key Concepts

Linear Equation in Slope-Intercept Form

This concept involves writing equations in the form y = mx + b, where m represents the rate of change (or slope) and b is the y-intercept, which is the starting value when the independent variable x is zero. It is fundamental for modeling linear relationships between two quantities.

Fixed and Variable Costs

In many real-world situations, costs consist of a fixed component that does not change with the level of usage, and a variable component that increases proportionally with usage. In a cost model, the fixed cost is represented by the y-intercept, while the variable cost per unit is reflected in the slope of the equation.

Interpreting Slope and Y-Intercept

The slope in a linear equation indicates the amount by which y (the dependent variable) changes for each unit change in x (the independent variable). The y-intercept represents the initial value of y when x is zero, allowing one to understand the starting point of the relationship.

Substitution in Linear Equations

Substitution involves replacing the variable x with a specific value to compute the corresponding value of y. This process helps interpret how a change in the independent variable affects the outcome, which is essential in practical applications such as cost analysis.

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