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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
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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
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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
⎝
⎠
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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⎠
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