1/24/2011 Section 4.1 The Rectangular Coordinate System Each point on a rectangular coordinate plane is represented by a pair of numbers called an ordered pair (x,y). Complete the given table for the equation, Complete the given table for the equation and then graph the equation. 30. 6x – 5y = 30 x y 0 0 3 ‐2 1 1/24/2011 x and y intercepts The x‐intercept is where the graph crosses the x‐axis The y‐intercept is where the graph crosses the y‐axis. To find the x‐intercept, substitute 0 for y and solve for x. This will give you an ordered pair of ( , ) the form (x,0). To find the y‐intercept, substitute 0 for x and solve for y. This will give you an ordered pair of the form (0,y). Find the x‐intercept and the y‐intercept for each of the equations. Using these graph the equation. 32. 5x + 2y = 10 2 1/24/2011 38. y = ‐3 42. x – 3y = 0 Finding the coordinates of the midpoint of a line segment when you know the coordinates of the two endpoints. Midpoint Formula When (x1,y1) and (x2,y2) are the endpoints, ⎛ x1 +x2 y1 + y2 ⎞ , ⎜ ⎟ 2 2 ⎝ ⎠ 3 1/24/2011 Page 198 Find the midpoint of each segment with the given endpoints. 46. (5,2) and (‐1,8) 48. (‐10,4) and (7,1) ⎛3 1⎞ ⎛1 7⎞ 56. ⎜ , − ⎟ and ⎜ , − ⎟ ⎝5 3⎠ ⎝2 2⎠ 4