Test 1 Review Problems A - MA 114-004 Fall 2013 Test 1...

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MA 114-004 Fall 2013 Test 1 Review Problems 1. Let 2 x - 6 y = - 6. (a) Write the linear equation in standard form. (b) Graph the linear equation. (c) Determine whether the following points are on the graph of the linear equation. i. (1 , 2) ii. (9 , 4) iii. ( - 6 , - 1) iv. (2 , 3) 2. Find the equation of the following lines. Give your answer in standard form. (a) Passing through the points (1 , 2) and (3 , - 4). (b) Passing through the point ( - 2 , 2) and parallel to y = 1 2 x - 1. (c) Passing through the point (2 , - 3) and perpendicular to y = 1 4 x + 7. 3. Consider the following system of inequalities 4 x + 2 y 16 x - 3 y - 17 2 x + 8 y 22 . (a) Rewrite the set of inequalities in standard form. (b) Graph the feasible set for the system. Find the exact coordinates of the vertices of the feasible set and label them on your graph. 4. The supply curve for WingDings is given by S : p = 0 . 0002 q + 0 . 06 and the demand curve for WingDings is given by D : p = - 0 . 0001 q + 34 . 98 where p is measured in dollars, and q of course is in units of WingDings. According to this model, at how many WingDings will the quantity produced stabilize, and what will be the price per WingDing when this happens? (Round to the nearest WingDing and/or cent if necessary). 5. Solve the following systems of linear equations using Gauss-Jordan elimination. (a) 3 x + 2 y + z = 7 2 x - y + 3 z = 14

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