EXAMPLE 7 Find the midpoint of the line segment with endpoints (3, 4) and (1, 2). Solution (x1, y1) (x2, y2) Begin by labeling the points: (3, 4), (1, 2). Substitute the values into the midpoint formula. Midpoint ax1 x2 2 , y1 y2 2 b a3 1 2 , 4 (2) 2 b Substitute values. a2 2 , 2 2 b (1, 1) Simplify. y 5 (3, 4) (1, 1) 5 5 5 YOU TRY 7 Find the midpoint of the line segment with endpoints (5, 2) and (1, 3). (1, 2) 7 Solve Applications Next we will see how a linear equation in two variables can be used to solve an application and how its graph can help us visualize the information that we get from the equation. EXAMPLE 8 The length of an 18-year-old female’s hair is measured to be 250 millimeters (mm) (almost 10 in.). The length of her hair after x days can be approximated by y 0.30x 250 where y is the length of her hair in millimeters. a) Find the length of her hair (i) 10 days, (ii) 60 days, and (iii) 90 days after the initial measurement, and write the results as ordered pairs. x b) Graph the equation. c) How long would it take for her hair to reach a length of 274 mm (almost 11 in.)? Solution a) The problem states that in the equation y 0.30x 250, x number of days after the hair was measured y length of the hair 1in millimeters2 www.mhhe.com/messersmith SECTION 4.1 Introduction to Linear Equations in Two Variables 147
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