Section 2.1 Linear Equations in Two Variables 139 Section 2.1 Practice Exercises Study Skills Exercise After getting a test back, it is a good idea to correct the test so that you do not make the same errors again. One recommended approach is to use a clean sheet of paper, and divide the paper down the middle vertically, as shown. For each problem that you missed on the test, rework the problem correctly on the left-hand side of the paper.Then give a written explanation on the right-hand side of the paper.To reinforce the correct procedure, return to the section of text from which the problem was taken and do several more problems. Take the time this week to make corrections from your last test. Vocabulary and Key Concepts 1. a. In a rectangular coordinate system, two number lines are drawn at right angles to each other.The horizontal line is called the -axis, and the vertical line is called the . b. A point in a rectangular coordinate system is defined by an pair, (x, y). c. In a rectangular coordinate system, the point where the x- and y-axes intersect is called the and is represented by the ordered pair . d. The x- and y-axes divide the coordinate plane into four regions called . e. A point with a positive x-coordinate and a y-coordinate is located in quadrant IV. f. In quadrant , both the x- and y-coordinates are negative. g. A linear equation in two variables is an equation that can be written in the form where A and B are not both zero. h. A point where a graph intersects the x-axis is called a(n) . i. A point where a graph intersects the y-axis is called a(n) . j. A line can be represented by an equation of the form x k, where k is a constant. k. A line can be represented by an equation of the form y k, where k is a constant. Concept 1: The Rectangular Coordinate System 2. Let a and b represent nonzero real numbers. a. An ordered pair of the form (0, b) represents a point on which axis? b. An ordered pair of the form (a, 0) represents a point on which axis? 3. Given the coordinates of a point, explain how to determine in which quadrant the point lies. 4. What is meant by the word ordered in the term ordered pair? 5. Plot the points on a rectangular coordinate system. (See Example 1.) 1 10, 42 2, 12 a. b. c. d. 110, 02 3, 02 e. a f. 14.1, 2.72 3 2 , 7 3 b Perform the correct math here. 2 4(5) 2 20 22 Explain the process here. Do multiplication before addition. 5 4 3 2 1 21 543 1 2 3 4 5 1 2 3 4 5 x y
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