1. Give 3 points that lie on the line 4x-y=6.
2. Give 3 points that lie on the line 3x+2y=6.
3. Give 3 points that lie on the line y= -4.
Can someone please help because I have no clue how to do these problems.
x=2
y=2
That doesn't make sense. The problem is give three points that lie on each line. Could someone please help me?
Sure! I'd be happy to help you solve these problems step by step.
1. To find points on the line 4x - y = 6, we can choose different values for either x or y, then solve for the other variable. Let's choose values for x and solve for y:
Let x = 0:
4(0) - y = 6
-y = 6
y = -6
So one point on the line is (0, -6).
Let x = 1:
4(1) - y = 6
4 - y = 6
-y = 6 - 4
-y = 2
y = -2
So another point on the line is (1, -2).
Let x = 2:
4(2) - y = 6
8 - y = 6
-y = 6 - 8
-y = -2
y = 2
So a third point on the line is (2, 2).
Therefore, three points on the line 4x - y = 6 are (0, -6), (1, -2), and (2, 2).
2. Similarly, to find points on the line 3x + 2y = 6, we can choose values for x, then solve for y:
Let x = 0:
3(0) + 2y = 6
2y = 6
y = 6/2
y = 3
So one point on the line is (0, 3).
Let x = 1:
3(1) + 2y = 6
3 + 2y = 6
2y = 6 - 3
2y = 3
y = 3/2
So another point on the line is (1, 3/2) or (1, 1.5).
Let x = 2:
3(2) + 2y = 6
6 + 2y = 6
2y = 6 - 6
2y = 0
y = 0
So a third point on the line is (2, 0).
Therefore, three points on the line 3x + 2y = 6 are (0, 3), (1, 1.5), and (2, 0).
3. For the line y = -4, the y-coordinate is always equal to -4, regardless of the value of x. Therefore, we can choose any values for x and the corresponding y-coordinate would still be -4.
Let's choose some values for x:
Let x = 0:
y = -4
So one point on the line is (0, -4).
Let x = 1:
y = -4
So another point on the line is (1, -4).
Let x = 2:
y = -4
So a third point on the line is (2, -4).
Therefore, three points on the line y = -4 are (0, -4), (1, -4), and (2, -4).
I hope this helps! Let me know if you have any further questions.