Use a graph to estimate the solution in each of the...

Use a graph to estimate the solution in each of the following. Be sure to use graph paper and a straightedge.
Becoming a member at Keeping Fit Club costs $\$ 75$ plus a monthly fee of $\$ 35 .$ Estimate how many months Kerry has been a member if he has paid a total of $\$ 215 .$

Key Concepts

Linear Equations

Linear equations represent relationships where one quantity changes at a constant rate with respect to another. They can be written in the form y = mx + b, where m is the slope representing the rate of change and b is the y-intercept representing the starting value. This form is useful for modeling situations with fixed initial values and consistent rates of change.

Fixed and Variable Costs

Many real-life scenarios, such as membership fees or service charges, involve a fixed cost added to a variable cost that depends on usage or time. The initial fixed cost does not change regardless of the duration, whereas the variable cost accumulates at a constant rate. Understanding this concept helps in forming a linear model to analyze the overall cost in terms of the number of units or time period.

Graphing Linear Relationships

Graphing is a visual method to represent linear equations by plotting them on coordinate axes. This approach helps in understanding how the dependent variable (such as cost) changes with respect to the independent variable (like time or quantity). The intersection of the graph of the equation with a horizontal line representing a specific total provides an estimate of the input value that meets the condition.

Graphical Estimation

Graphical estimation involves using the visual intersection or intercept on a plotted graph to acquire an approximate solution to an equation. It is particularly effective for problems where precise calculations may not be necessary or when estimating is more practical, and it emphasizes understanding where different linear relationships meet.

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