y-intercept: Let x 0, and solve for y. y 12 (0) 1 y 0 1 1 The y-intercept is (0, 1). We must fi nd another point. Let’s look closely at the equation y 12 x 1. The coeffi cient of x is 12 . If we choose a value for x that 12 is a multiple of 2 (the denominator of the fraction), then x will not be a fraction. Let x 2. y 12 x 1 y 12 (2) 1 y 1 1 y 2 The third point is (2, 2). Plot the points, and draw the line through them. 5 x t t 2 y t t 1 5 5 y x 1 1 YOU TRY 4 Graph y 3x 6 by fi nding the intercepts and one other point. 5 Graph Linear Equations of the Forms x a and y b The equation x a is a linear equation in two variables since it can be written in the form x 0y a. The same is true for y b. It can be written as 0x y b. Let’s see how we can graph these equations. EXAMPLE 5 Graph x 3. Notice that if x is constant, then the graphed line is vertical (parallel to the y-axis). y 5 2 2 2 Solution The equation is x 3. (This is the same as x 0y 3.) x 3 means that no matter the value of y, x always equals 3. We can make a table of values where we choose any value for y, but x is always 3. x y 3 0 3 1 3 2 y Plot the points, and draw a line through them. The graph of x 3 is a vertical line. 5 x 1 5 5 5 We can generalize the result as follows: x 2 Property The Graph of x a If a is a constant, then the graph of x a is a vertical line going through the point (a, 0). x www.mhhe.com/messersmith SECTION 4.1 Introduction to Linear Equations in Two Variables 145
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