Mat222 Week 2 Assignment

Running head: TWO-VARIABLE

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Two-Variable Inequalities Janice Johnson MAT222: Intermediate Algebra Dr. Eric Bienstock December 06, 2014

TWO-VARIABLE Two-Variable Inequalities This week’s work is a continuation from our topic of functions and relationships between variables. We will be using a practical application of two-variable inequalities this week. There will be graphic representations along with the dependent and independent variables. There are answers that would work with our problem because of the inequality. For this paper I am using the problem #68 on page 539 in our textbook (Dugopolski, 2012).

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Shipping restrictions. The accompanying graph shows all of the possibilities for the total number of refrigerators and the total number of televisions that will fit into an 18-wheeler. The maximum number of refrigerators this truck can carry would be 110 units; there could be no televisions with this load. If the truck was carrying televisions it could have 330 units to haul and no refrigerators. The following graph shows that refrigerators are represented by x and the televisions are represented with the y. Working with 2 points on the graph (0, 330) and (110, 0) we will use to find the slope of the line.

(0,330)

(110, 0)

To find the slope you start with the point slope form: y –y1 = m (x – x1) y1 – y2 330 - 0 330 _____ = _______ = - _____ = -3 x1 – x2 0 – 110 110

TWO-VARIABLE The steps to finding the linear inequality using the slope point form would be as follows: y – 330 = -3 (x – 0) y= -3x + 330 y+ 3x ≥ 330 symbol to less than or equal. Substitute point (0, 330) and m with previous slope Next is to add 300 to both sides Add 3x to both sides after that. We would change the equal

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The graph shows that it is a part of the solution by using a solid line instead of a dashed line. Any time there is a solid bar and there is an inequality symbol the solution will be true when there is an equal to bar. The next question in this...