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messersmith_power_intermediate_algebra_1e_ch4_7_10

We get the table of values x y 0 2 2 3 4 0 x y 5 (0, 2) (2, 3) x 2y 4 (4, 0) 5 5 5 Plot the points (0, 2), (2, 3), and (4, 0), and draw the line through them. If possible, use graph paper when graphing lines. Don’t forget to label the x- and y-axes and to draw arrowheads on both ends of your lines. YOU TRY 3 Graph each line. a) 3x 2y 6 b) y 4x 8 4 Graph a Linear Equation in Two Variables by Finding the Intercepts In Example 3, the line crosses the x-axis at 4 and crosses the y-axis at 2. These points are called intercepts. What is the y-coordinate of any point on the x-axis? It is zero. Likewise, the x-coordinate of any point on the y-axis is zero. y y-intercept x-intercept Notice that the y-intercept is where x 0, and the x-intercept is where y 0. Definition The x-intercept of the graph of an equation is the point where the graph intersects the x-axis. The y-intercept of the graph of an equation is the point where the graph intersects the y-axis. Procedure Finding Intercepts To fi nd the x-intercept of the graph of an equation, let y 0 and solve for x. To fi nd the y-intercept of the graph of an equation, let x 0 and solve for y. x Finding intercepts is very helpful for graphing linear equations in two variables. EXAMPLE 4 Graph y 1 2 x 1 by fi nding the intercepts and one other point. Solution We will begin by fi nding the intercepts. x-intercept: Let y 0, and solve for x. 0 12 x 1 1 12 x Multiply both sides by 2 to solve for x. 2 x The x-intercept is (2, 0). 144 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith


messersmith_power_intermediate_algebra_1e_ch4_7_10
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