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Example: Solving Veronica's Part-Time Jobs Application with a Linear Inequality in Two Variables
To find valid solutions for a financial requirement involving two distinct sources of income, an algebraic model using a linear inequality in two variables can be graphed. Consider Veronica, whose job at a day spa pays $10 an hour and whose administrative assistant job pays $17.50 an hour. She needs to earn at least $280 a week. Translate into an inequality: Let be the day spa hours and be the administrative assistant hours. The conditional model is . Graph the inequality: Find the boundary line by converting to slope-intercept form. Subtracting gives . Dividing by 17.50 yields , which simplifies to . Graph the solid boundary line corresponding to this equation and shade the solution region above the line. Any valid ordered pair within the shaded area represents a combination of hours Veronica can work at each job to earn at least $280.
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Example: Solving a Part-Time Job Income Application with a Linear Inequality in Two Variables
Example: Solving Hugh's Part-Time Jobs Application with a Linear Inequality in Two Variables
Example: Solving Veronica's Part-Time Jobs Application with a Linear Inequality in Two Variables
Solving a System of Linear Inequalities by Graphing
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Veronica works two part-time jobs to meet her weekly budget requirements. She earns per hour at a day spa (where is the number of hours worked) and {}17.50 per hour as an administrative assistant (where is the number of hours worked). To cover her expenses, she must earn a minimum of per week. Her situation is modeled by the linear inequality .
Match each component of this algebraic model to its corresponding real-world meaning in Veronica's financial plan.
Veronica uses the linear inequality to plan her weekly work schedule across two jobs. When she graphs this inequality to visualize her options, what do the coordinates (x, y) of any point located in the shaded solution region represent?
In the context of Veronica's income model, she uses the linear inequality to represent her goal of earning a minimum of per week. True or False: When graphing this inequality, the boundary line should be drawn as a solid line to show that earning exactly is a valid solution.
Veronica is planning her weekly work schedule to ensure she earns a minimum of 280 dollars. She uses the inequality to model her income from two jobs. To visualize her options on a graph, she needs to convert this inequality into slope-intercept form (). Arrange the following algebraic steps in the correct order to complete the conversion.
Recalling the Algebraic Model for Veronica's Income
Veronica is managing her work hours across two part-time jobs to meet her weekly budget. She models her income requirement using the linear inequality , which can be rewritten in slope-intercept form as . Because her weekly earnings must be greater than or equal to her budget goal, the set of all valid combinations of hours she can work is represented on a coordinate plane by shading the region ____ the solid boundary line.
Veronica's Multi-Job Budgeting and Income Strategy