• If given two ordered pairs, we can find the slope by substituting the x and y coordinates of the two points into the formula, m = y2 - y1 x2 - x1 , and simplifying. 3. The slope tells us the direction of the line. • A positive slope indicates the line goes up from left to right. • A negative slope indicates the line goes down from left to right. • A zero slope indicates the line is horizontal. • An undefined slope indicates the line is vertical. 4. The graph of a line can be obtained using the slope and y-intercept. Plot the y-intercept and use the slope to move to another point on the line. GRAPHING CALCULATOR SKILLS The graphing calculator can be used to verify our graphs as was illustrated in the previous section. We can also verify the slope of a line by examining the table of solutions and the graph of an equation. Example: Graph y=- 2 3 x + 2 using its slope and y-intercept. ( ) 2 4 3 T u n + 2 From the graph, we can verify that the slope is - 2 3 since the movement between points is down 2 and right 3. Down 2 (0, 2) Right 3 RA H M 4 Examining the table also confirms the slope of the line. As the y-values decrease by 0.66667, the x-values increase by 1 unit or as the y-values decrease by 2 units, the x-values increase by 3 units. y-values decrease by 2 x-values increase by 3 2nd RA H �� ���������������� �������� EXERCISE SET Write About It! Use complete sentences to explain the meaning of each process. 1. Finding the slope of line between two points 2. Finding the slope of line from a linear equation 3. Finding the slope of a horizontal line 4. Finding the slope of a vertical line Determine if each statement is true or false. If a statement is false, provide an explanation. 5. The slope of the line 2x + 5y = 10 is 2. 6. If the slope of a line is - 4 3 , we would move down 4 units and left 3 units to get to another point on the line. 7. The slope of the line x = 5 is 0. 8. The slope of the line y = 4 is undefined. 9. The slope of the line through (3, 5) and (4, -1) is - 1 6 . 10. The slope of the line through (-2, -3) and (2, -1) is undefined. Practice Makes Perfect! Use the slope formula to determine the slope of the line between each pair of points. (See Objective 1.) 11. (-2, 3) and (4, 5) 12. (1, -7) and (-3, 7) 13. (-6, -2) and (0, 4) 14. (5, 0) and (-4, 2) 15. (-4, 3) and (-4, 5) 16. (3, 7) and (3, -2) 17. (1, -8) and (4, -8) 18. (-2, 6) and (5, 6) 19. a- 1 6 , 1 4 b and a1 3 , - 5 4 b 20. a- 1 3 , - 5 2 b and a2 3 , 3 2 b 21. a7 3 , 1 2 b and a- 2 3 , - 3 2 b 22. a1 2 , - 2 5 b and a- 1 4 , 4 5 b 236 Chapter 3 Linear Equations in Two Variables
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