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
In problem #3, pick any three value of x. y will always be -4. It is a horizontal line.
For problems 1 and 2, pick any three values of x and compute the corresponding value of y using the formula provided.
For example, if x = 0, use the 4x -y = 6 formula to determine that y = -6. Therefore
x = 0, y = -6 is one point on the line whose formula is 4x -y = 6
Sure! I can explain how to find points that lie on each of these lines.
1. Line 4x - y = 6:
To find points on this line, you can choose any value for x and then solve for the corresponding y-coordinate.
Let's choose x = 0:
Substituting x = 0 into the equation, we get:
4(0) - y = 6
Simplifying the equation, we have:
-y = 6
To isolate y, we multiply both sides of the equation by -1 (to change the sign):
y = -6
So, one point on the line is (0, -6).
Now let's choose x = 2:
Substituting x = 2 into the equation, we get:
4(2) - y = 6
Simplifying the equation, we have:
8 - y = 6
To isolate y, we subtract 8 from both sides of the equation:
-y = 6 - 8
-y = -2
Since -y is equivalent to y multiplied by -1, we have:
y = 2
So, another point on the line is (2, 2).
Finally, let's choose x = -3:
Substituting x = -3 into the equation, we get:
4(-3) - y = 6
Simplifying the equation, we have:
-12 - y = 6
To isolate y, we add 12 to both sides of the equation:
-y = 6 + 12
-y = 18
Again, multiplying both sides by -1, we get:
y = -18
So, the third point on the line is (-3, -18).
Therefore, three points lying on the line 4x - y = 6 are (0, -6), (2, 2), and (-3, -18).
2. Line 3x + 2y = 6:
Following a similar process, we can find points on this line by selecting different x-values and solving for the corresponding y-coordinate.
Let's choose x = 0:
Substituting x = 0 into the equation, we get:
3(0) + 2y = 6
Simplifying the equation, we have:
2y = 6
To isolate y, we divide both sides of the equation by 2:
y = 6/2
y = 3
So, one point on the line is (0, 3).
Now let's choose x = 1:
Substituting x = 1 into the equation, we get:
3(1) + 2y = 6
Simplifying the equation, we have:
3 + 2y = 6
To isolate y, we subtract 3 from both sides of the equation:
2y = 6 - 3
2y = 3
Dividing both sides by 2, we have:
y = 3/2
So, another point on the line is (1, 3/2) or (1, 1.5).
Finally, let's choose x = -2:
Substituting x = -2 into the equation, we get:
3(-2) + 2y = 6
Simplifying the equation, we have:
-6 + 2y = 6
To isolate y, we add 6 to both sides of the equation:
2y = 6 + 6
2y = 12
Dividing both sides by 2, we get:
y = 12/2
y = 6
So, the third point on the line is (-2, 6).
Thus, three points lying on the line 3x + 2y = 6 are (0, 3), (1, 1.5), and (-2, 6).
3. Line y = -4:
In this case, the equation is already in the form y = constant. This tells us that all points on the line will have the same y-coordinate, which is -4 in this case.
To find three points on this line, we can choose any three different x-coordinates and use y = -4 for each of them.
Let's choose x = 0:
So, the point is (0, -4).
Now let's choose x = 1:
The point is (1, -4).
Finally, let's choose x = -1:
The point is (-1, -4).
Therefore, three points lying on the line y = -4 are (0, -4), (1, -4), and (-1, -4).