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226 Chapter 3 Linear Equations in Two Variables �� ������������������������ The Slope of a Line ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Use the slope formula to determine the slope of a line. 2. Use the slope-intercept form of a line to find its slope and y-intercept. 3. Graph a line given its slope and y-intercept. 4. Troubleshoot common errors. In Section 3.2, we learned how to graph lines such as y = 2x and y = 1 2 x, which are shown in the following graphs. In this section, we will discuss a property of lines. This property will answer the question, “How do the following graphs of the two lines compare to one another?” 2 2 4 4 –2 –4 –2 –4 x y y = 2x 2 2 4 4 –2 –4 –2 –4 x y y = x 12 Observing the lines, we can see that the line on the left is steeper than the line on the right. A line’s steepness, or slope, can be used to describe its graph. In this section, we will explore the slope of a line and how we can determine it. The Slope Formula In Section 3.2, we graphed the line y = 2x - 4. Let’s explore some of its solutions and how they relate to the graph of the line. x y Change in x Change in y Change in y Change in x 0 2(0) - 4 = -4 1 2(1) - 4 = -2 1 - 0 = 1 -2 - (-4) = 2 2 1 = 2 2 2(2) - 4 = 0 2 - 1 = 1 0 - (-2) = 2 2 1 = 2 3 2(3) - 4 = 2 3 - 2 = 1 2 - 0 = 2 2 1 = 2 The y-values of the solutions in the table increase by 2 units every time the x-values of the solutions increase by 1 unit. This can be seen from the graph in that as we move 1 unit to the right, the graph rises 2 units. Right 1 Rise 2 (3, 2) (2, 0) (1, –2) (0, –4) 4 2 4 –2 –1 –4 –6 x y The ratio of these changes, Change in y (vertical change) Change in x (horizontal change) , is called the slope of the line. So, the slope of the line y = 2x - 4 is 2. Slope = change in y change in x = 2 1 = 2 Objective 1 ▶ Use the slope formula to determine the slope of a line.


hendricks_beginning_algebra_1e_ch1_3
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