# Linear equation

Running header should use a shortened version of the title If the title Is long. Page number is located at right margin. (full title; centered horizontally & vertically) Two-variable Inequalities John Q. Student Assignment Instructor’s Name Date Running Header Two-variable Inequalities (title required on flrst line) Continuing last week’s topic of functions and relationships between variables, this week’s work examines a practical application of two-variable inequalities.

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As the ame implies, there are independent and dependent variables, as well as graphic representations of the solutions. Because of the inequality, the graphs and solutions demonstrate a range of possible answers that would work in the given situation. This problem is similar to #68 on page 539 (Dugopolski, 2012) for purposes of demonstrating the math needed for this writing assignment. A shipping container can carry maximum of 125 sofas and no recliners, or maximum of no sofas and 275 recliners. Study the graph and write an equation to fit the line.

Pretend the triangle egion is shaded in and change the equation to an inequality describing this region. The diagram is showing the sofas on the x axis and the recliners on the y axis. There are two points on the graph, (275, O) and (O, 125), so we can compute the slope of this line. The slope Is 3 The point-slope form of a linear equation to write the equation Itself can now be used. These are the steps we take to arrive at our linear inequality. Start with the Substitute the slope for m and (275, O) for the x and y.

Use distributive property and then add 275 to both sides. Multiply both sides by 5. Add 1 lx to both sides and change to less than or equal to symbol. The graph has a solid line rather than a dotted line indicating that points on the line itself are part of the solution set. This will be true anytime the inequality symbol has the equal to bar. There are two more questions to answer in this section: 1 . Will the shipping container hold 80 sofas and 200 recliners? In other words is the point (80, 200) in the solution region.