Chapter 3 Review Exercises 283 6. If a point lies on the graph of an equation, it is a(n) of the equation. 7. We used and to solve application problems. From these representations, must be identified to answer questions. SECTION 3.2 Graphing Linear Equations 8. The standard form of a linear equation in two variables is . 9. To graph a line by plotting points, points are required. However, a total of points is recommended so that one of the points serves as a check. 10. The point where a graph crosses the x-axis is called the . To find this point, set = 0 and solve the resulting equation. The point where a graph crosses the y-axis is called the . To find this point, set = 0 and solve the resulting equation. 11. If the value of the constant in a linear equation equals zero, then the graph of the equation will pass through the . To graph such an equation, . 12. The equation of a horizontal line has the form . 13. The equation of a vertical line has the form . SECTION 3.3 The Slope of a Line 14. The slope of a line measures the of the line. 15. The slope is defined as the ratio of the change to the change. It is also called over . 16. The slope-intercept form of a line is . The m represents the and b represents the . 17. To graph a line using the slope and y-intercept, plot the first. From this point, use the to move to another point on the line. For instance, a slope of 4 3 would mean to and . 18. A horizontal line has a slope of and a vertical line has a slope that is . 19. The slope formula is . 20. A positive slope corresponds to a line that is . A negative slope corresponds to a line that is . A slope of zero corresponds to a line. An undefined slope corresponds to a line. SECTION 3.4 More About Slope 21. In application problems, the value of b represents the value. The value m represents the . 22. Two lines are if they have the same . 23. Two lines are if their slopes are reciprocals. SECTION 3.5 Writing Equations of Lines 24. To write the equation of a line, we must know the and at least one . The form of a line or the form of a line can be used to find the equation. SECTION 3.6 Functions 25. A(n) is a set of ordered pairs. The set of x-values is the , and the set of y-values is the . 26. A is a relation in which each input value corresponds to output value. 27. The line test can be used to determine if a graph represents a function. If every vertical line touches at most on the graph, then the graph is a function. 28. In function notation, we use the symbol for y. 29. To write a linear equation in two variables in function notation, we must first solve the equation for . 30. If f (a) = b, then the point is on the graph of f (x). CHAPTER 3 / REVIEW EXERCISES SECTION 3.1 Determine algebraically if the given ordered pair is a solution of the equation. (See Objective 1.) 1. (1, -1); 3x - 2y = 5 2. (-3, -0.75); x + 6y = -7.5 3. (-2, 1); y = u3 - xu 4. (4, 1); y = -x2 + 8x - 15 5. (-2, 0); y = x - 2 x + 2 6. (0, 3); y = 2x - 3 x + 1 Plot each ordered pair on the Cartesian coordinate system and state the quadrant or axis where each point is located. (See Objective 2.) 7. (-5, 1) 8. (2, 0) 9. (-3, -2.5) 10. a7 2 , 4b 11. (0, -4) 12. (1, -6) Identify each point plotted on the coordinate system and state the quadrant or axis where each point is located. (See Objective 2.) 2 2 4 4 6 A C B D –2 F E –4 –2 –4 x y 13. A 14. B 15. C 16. D 17. E 18. F
hendricks_beginning_algebra_1e_ch1_3
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