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

points are coordinates, so any set of numbers (x,y) that fall on the line in each question.

for questions 1&2, pick a number for x (try 1,2,3) and then solve for y. for the first question that would be:

x=1:
4*(1)-y=6
4-y=6
y=2
one possible answer: (1,2)

keep going, and see if you can get 3 by yourself

oops, lost that negative sign:

4-y=6
y=-2
one possible answer: (1,-2)

List any three points that lie on the line , x=2

1. Sure, here are three points that lie on the line 4x-y=6:

- Point 1: Let's say x = 0. If we substitute x = 0 in the equation, we get 4(0) - y = 6, which simplifies to -y = 6. Solving for y, we have y = -6. So, one point on the line is (0, -6).

- Point 2: Let's take another value for x, say x = 2. Substituting x = 2 in the equation, we get 4(2) - y = 6, which simplifies to 8 - y = 6. Solving for y, we have y = 2. So, another point on the line is (2, 2).

- Point 3: Lastly, let's choose one more value for x, say x = -3. Substituting x = -3 in the equation, we get 4(-3) - y = 6, which simplifies to -12 - y = 6. Solving for y, we have y = -18. So, another point on the line is (-3, -18).

2. Now, let's find three points that lie on the line 3x + 2y = 6:

- Point 1: Let's say x = 0. Substituting x = 0 in the equation, we get 3(0) + 2y = 6, which simplifies to 2y = 6. Solving for y, we have y = 3. So, one point on the line is (0, 3).

- Point 2: Let's take another value for x, say x = 2. Substituting x = 2 in the equation, we get 3(2) + 2y = 6, which simplifies to 6 + 2y = 6. Solving for y, we have y = 0. So, another point on the line is (2, 0).

- Point 3: Lastly, let's choose one more value for x, say x = -3. Substituting x = -3 in the equation, we get 3(-3) + 2y = 6, which simplifies to -9 + 2y = 6. Solving for y, we have y = 7.5. So, another point on the line is (-3, 7.5).

3. Finding three points on the line y = -4 is simple since y is always -4 on this line:

- Point 1: The first point on the line is (0, -4).

- Point 2: The second point on the line is (1, -4).

- Point 3: The third point on the line is (-2, -4).

I hope that helps! If you have any other questions, feel free to ask, but remember, I'm here to lighten the mood, not just answer questions!

Sure! I can help you with these problems. To find points that lie on a given line, we can use a method called substitution.

1. Let's solve the equation 4x - y = 6 for y, by isolating y on one side of the equation.

Start with: 4x - y = 6
Add y to both sides: 4x = y + 6
Now, subtract 6 from both sides: 4x - 6 = y

We have isolated y, so we can substitute different values for x and find the corresponding values of y to get the points. Let's choose three values for x and find their corresponding y-values:

a) Let's choose x = 0:
Substituting x = 0 into the equation, we get:
4(0) - 6 = y
-6 = y

Therefore, the point (0, -6) lies on the line 4x - y = 6.

b) Let's choose x = 1:
Substituting x = 1 into the equation, we get:
4(1) - 6 = y
-2 = y

Therefore, the point (1, -2) lies on the line 4x - y = 6.

c) Let's choose x = 2:
Substituting x = 2 into the equation, we get:
4(2) - 6 = y
2 = y

Therefore, the point (2, 2) lies on the line 4x - y = 6.

So, the three points that lie on the line 4x - y = 6 are (0, -6), (1, -2), and (2, 2).

2. Let's solve the equation 3x + 2y = 6 for y, using the same method as above.

Start with: 3x + 2y = 6
Subtract 3x from both sides: 2y = -3x + 6
Divide both sides by 2: y = (-3/2)x + 3

Now, let's choose three different values for x and find their corresponding y-values:

a) Let's choose x = 0:
Substituting x = 0 into the equation, we get:
y = (-3/2)(0) + 3
y = 3

Therefore, the point (0, 3) lies on the line 3x + 2y = 6.

b) Let's choose x = 1:
Substituting x = 1 into the equation, we get:
y = (-3/2)(1) + 3
y = 1.5

Therefore, the point (1, 1.5) lies on the line 3x + 2y = 6.

c) Let's choose x = 2:
Substituting x = 2 into the equation, we get:
y = (-3/2)(2) + 3
y = 0

Therefore, the point (2, 0) lies on the line 3x + 2y = 6.

So, the three points that lie on the line 3x + 2y = 6 are (0, 3), (1, 1.5), and (2, 0).

3. The equation y = -4 represents a horizontal line at the y-coordinate -4. Since y remains constant, we can choose any x value and the corresponding y-value will always be -4.

a) Let's choose x = 0:
The y-value is always -4, so the point is (0, -4), which lies on the line y = -4.

b) Let's choose x = 1:
The y-value is still -4, so the point is (1, -4), which lies on the line y = -4.

c) Let's choose x = -2:
The y-value remains -4, so the point is (-2, -4), which lies on the line y = -4.

So, the three points that lie on the line y = -4 are (0, -4), (1, -4), and (-2, -4).