1. Name the domain and range for the relation shown in each graph D = {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? linear nonlinear linear nonlinear Example 2-1a

3. Slope-intercept form y = mx + b f(x) = mx + b m is the slope of the line b is the y-intercept What are the slope and y-intercept of the line ? Slope = 3 y-intercept = -9 Example 2-1d

4. The graph of a linear equation is a line. Graph the line y-intercept = -9 Slope = 3 Slope = ΔyΔx Example 2-1d

6. A is positive

7. A and B are not both zero3x + 5y = -2 is in standard form Example 2-1d

8. Write the equation in standard form. Identify A, B, and C. Ax + By = C Simplified? 2 2 2 Example 2-3c

9. Write the equation in standard form. Identify A, B, and C. Ax + By = C Simplified? 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 = 0 x-intercept -2x + 0 – 4 = 0 -2x – 4 = 0 -2x = 4 x = -2 The x-intercept is -2 (-2, 0) y-intercept -2(0) + y – 4 = 0 0 + y – 4 = 0 y – 4 = 0 y = 4 The y-intercept is 4 (0, 4) Example 2-4b

12. (0, 4) (–2, 0) Graph -2x + y – 4 = 0 x-intercept : –2 y-intercept: 4 Example 2-4c

13. Slope m = vertical change Horizontal change m = ΔyΔx m = rise run Any 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 slope Positive slope Zero slope Negative slope Undefined slope

16. Graph x = 1 Graph 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 = 10 4x – 2y =10 -2y = -4x + 10 -2 -2 -2 y = 2x – 5 m = 2 , b = -5 Parallel slope = 2

19. Graph the line that passes through (2, 1) that is perpendicular to the graph of 4x – 2y = 10 4x – 2y =10 -2y = -4x + 10 -2 -2 -2 y = 2x – 5 m = 2 , b = -5 Perpendicular slope = -1/2