Alg2 lesson 2.2 and 2.3
- 1. Name the domain and range for the relation shown in each graphD = {x | x is a real number}D = {x | x is a real number}R = {y | y ≥ 0}R = {y | y ≥ -2}Lesson 2 Contents
- 2. In a linear equation, each term is either a constant or the product of a constant and (the first power of) a single variable.Which of these represent linear functions?linearnonlinearlinearnonlinearExample 2-1a
- 3. Slope-intercept form y = mx + b f(x) = mx + bm is the slope of the lineb is the y-interceptWhat are the slope and y-intercept of the line ?Slope = 3y-intercept = -9Example 2-1d
- 4. The graph of a linear equation is a line.Graph the line y-intercept = -9Slope = 3Slope = ΔyΔxExample 2-1d
- 5. Standardform Ax + By = C A, B and C are integers (not fractions!)
- 6. A is positive
- 7. A and B are not both zero3x + 5y = -2 is in standard formExample 2-1d
- 8. Write the equation in standard form. Identify A, B, and C. Ax + By = CSimplified?2 2 2Example 2-3c
- 9. Write the equation in standard form. Identify A, B, and C. Ax + By = CSimplified?Example 2-3a
- 10. Write the equation in standard form. Identify A, B, and C. Ax + By = C-3 (-3)Simplified?Example 2-3b
- 11. Find the x- and y- intercepts of -2x + y – 4 = 0x-intercept-2x + 0 – 4 = 0-2x – 4 = 0-2x = 4x = -2The x-intercept is -2 (-2, 0)y-intercept-2(0) + y – 4 = 00 + y – 4 = 0y – 4 = 0y = 4The y-intercept is 4 (0, 4)Example 2-4b
- 12. (0, 4)(–2, 0)Graph -2x + y – 4 = 0x-intercept : –2y-intercept: 4Example 2-4c
- 13. Slope m = vertical change Horizontal change m = ΔyΔx m = rise runAny two points on a line can be used to determine its slope.
- 14. Find the slope of a line passing through (-3,5) & (2,1)
- 15. Classification of lines by slopePositive slopeZero slopeNegative slopeUndefined slope
- 16. Graph x = 1Graph y = 3
- 17. Parallel lines have equal slopes.Perpendicular lines have slopes that are opposite reciprocals.
- 18. Graph the line that passes through (2, 1) that is parallel to the graph of 4x – 2y = 104x – 2y =10-2y = -4x + 10 -2 -2 -2 y = 2x – 5m = 2 , b = -5Parallel slope = 2
- 19. Graph the line that passes through (2, 1) that is perpendicular to the graph of 4x – 2y = 104x – 2y =10-2y = -4x + 10 -2 -2 -2 y = 2x – 5m = 2 , b = -5Perpendicular slope = -1/2