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3x - 2y = 6 , 2x + 3= 6 are perpendicular lines but i need 3 ordered pairs for each. I used the m= y2-y1/x2-x1 method to establish that the slopes = -1. Any suggestions for ordered pairs for each line is much appreciated.

User Icon for drwls drwls answered
15 years ago

You must have written the second equation incorrectly. It needs a "y" term. It the productsa of the slopes, not the slopes themselves that must be -1.

Picking an ordered pair is just a matter of picking x and computing y, for any x that you want. Two ordered pairs define a straight line.

User Icon for Explain Bot Explain Bot answered
11 months ago

To find three ordered pairs for each line, we need to solve the equations and find the corresponding values of x and y. Let's start with the equation 3x - 2y = 6.

Step 1: Solve for y in terms of x:
3x - 2y = 6
-2y = -3x + 6
y = (3/2)x - 3

Now, let's substitute different values of x into this equation to find the corresponding y values.

For Line 1:
Ordered Pair 1: Let x = 0
y = (3/2)(0) - 3
y = -3

Ordered Pair 2: Let x = 1
y = (3/2)(1) - 3
y = -1.5 - 3
y = -4.5

Ordered Pair 3: Let x = 2
y = (3/2)(2) - 3
y = 3 - 3
y = 0

Therefore, the three ordered pairs for Line 1 are (0, -3), (1, -4.5), and (2, 0).

Now, let's move to the second equation: 2x + 3 = 6.

Step 2: Solve for x:
2x + 3 = 6
2x = 6 - 3
2x = 3
x = 3/2
x = 1.5

Substitute different values of x into the equation to find the corresponding y values:

For Line 2:
Ordered Pair 1: Let x = 0
2(0) + 3 = 6
3 = 6 (False)

Ordered Pair 2: Let x = 1
2(1) + 3 = 6
2 + 3 = 6 (False)

Ordered Pair 3: Let x = 2
2(2) + 3 = 6
4 + 3 = 6 (False)

It seems that the second equation does not define a line. Therefore, it is not possible to find three ordered pairs for Line 2.

In conclusion, the three ordered pairs for Line 1 are (0, -3), (1, -4.5), and (2, 0). However, we cannot find three ordered pairs for Line 2 as it does not define a line.