Section 2.1 Linear Equations in Two Variables 133 The completed list of ordered pairs is as follows.To graph the equation, plot the three solutions and draw the line through the points (Figure 2-6). 10, 22 2 Skill Practice 6. Graph the equation y 1 3 x1. Hint: Select values of x that are multiples of 3. 5 4 3 2 1 21 1 Figure 2-6 x y 0 2 4 0 (4, 0) 12, 12 1 543 1 2 3 4 5 2 3 4 5 x y y x 2 1 2 (4, 0) (0, 2) (2, 1) Answer 6. 5 4 3 2 1 543 1 2 3 4 5 21 1 2 3 4 5 x y y x 1 1 3 4. x- and y-Intercepts For many applications of graphing, it is advantageous to know the points where a graph intersects the x- or y-axis.These points are called the x- and y-intercepts. In Figure 2-5, the x-intercept is (5, 0). In Figure 2-6, the x-intercept is (4, 0). In general, a point on the x-axis must have a y-coordinate of zero. In Figure 2-5, the y-intercept is (0, 3). In Figure 2-6, the y-intercept is (0, 2). In general, a point on the y-axis must have an x-coordinate of zero. Definition of x- and y-Intercepts An x-intercept* is a point 1a, 02 where a graph intersects the x-axis. (See Figure 2-7.) A y-intercept is a point 10, b2 where a graph intersects the y-axis. (See Figure 2-7.) *In some applications, an x-intercept is defined as the x-coordinate of a point of intersection that a graph makes with the x-axis. For example, if an x-intercept is at the point (3, 0), it is sometimes stated simply as 3 (the y-coordinate is understood to be zero). Similarly, a y-intercept is sometimes defined as the y-coordinate of a point of intersection that a graph makes with the y-axis. For example, if a y-intercept is at the point (0, 7), it may be stated simply as 7 (the x-coordinate is understood to be zero). x y (0, b) (a, 0) Figure 2-7 To find the x- and y-intercepts from an equation in x and y, follow these steps: Determining the x- and y-Intercepts from an Equation Given an equation in x and y, • Find the x-intercept(s) by substituting y 0 into the equation and solving for x. • Find the y-intercept(s) by substituting x 0 into the equation and solving for y.
miller_intermediate_algebra_4e_ch1_3
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