Section 3.4 More About Slope 239 PIECE IT TOGETHER ���������������������������������������������� Determine algebraically if the ordered pair is a solution of the equation. (Section 3.1, Objective 1) 1. (6, 2); y = ux - 4u 2. (7, -4); 8x - 2y = 62 Identify the quadrant or axis where each point is located. (Section 3.1, Objective 2) 3. (-8.9, -1) 4. a7 8 , - 5 6 b 5. (-5, -1) 6. (9, 4) Use the given graph of an equation to determine if each ordered pair is a solution of the equation. (Section 3.1, Objective 4) 7. (0, 3) 8. (2, -3) 2 2 4 4 8 –2 –4 –2 –4 x y Graph each equation. (Section 3.2, Objectives 2–4) 9. y = 4x + 2 10. y = -5x + 5 11. 4x - y = 0 12. y = -7x 13. 3x + 8 = 0 14. 2y - 11 = 0 Use the slope formula to determine the slope of the line between each pair of points. (Section 3.3, Objective 1) 15. (-2, 3) and (4, 7) 16. (-2, 8) and (5, 8) Write each equation in slope-intercept form, if necessary. State the slope and y-intercept of the line from its equation. Write the y-intercept as an ordered pair. Explain how the x- and y-values change with respect to one another. (Section 3.3, Objective 2) 17. 3x - 2y = 6 18. 5x + 3y = -15 Graph each line using its slope and y-intercept. Label two points on the graph. (Section 3.3, Objective 3) 19. y = 1 4 x - 1 20. x - 7y = 14 �� �������������������������� More About Slope The depreciated value of a truck is given by y = -4000x + 32,000, where x is the age of the truck. How does the truck’s value change each year? What is the initial value of the truck? In this section, we will learn how to interpret the meaning of the slope and y-intercept in the context of applications. We will also examine the relationships between parallel and perpendicular lines. Interpret the Meaning of the Slope and y-Intercept When a linear equation in two variables represents a real-world situation, the slope and y-intercept have practical meanings that relate to the situation. In the equation y = mx + b, we know that • The point (0, b) is the y-intercept. Therefore, the value b is the beginning or initial value. • The slope m represents a rate of change. The slope tells us how the y-values change with respect to a change in x. When dealing with lines, the slope is constant. So, lines are used to describe quantities that change at a constant rate. ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Interpret the meaning of the slope and y-intercept in real-world applications. 2. Determine the slope in real-world applications. 3. Determine if two lines are parallel or perpendicular. 4. Graph parallel or perpendicular lines if given the equation of one line and a point on the line parallel or perpendicular to it. 5. Troubleshoot common errors. �� ������������������������ ������������������ Interpret the meaning of the slope and y-intercept in the context of each situation. Use the slope and y-intercept to create a table of three ordered pairs that satisfy the given equation. 1a. Jose’s salary as an engineer can be given by y = 3500x + 45,000, where x is the number of years he has worked for the company. Objective 1 ▶ Interpret the meaning of the slope and y-intercept in real-world applications.
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