Please help me on linear relation. I have tries but I am really stuck on the creating table and graphing.

1. provide a table of six values that represent a linear relation. All the y-values must be less then zero.

2. provide a table of six values that does not represent a linear relation. All the y-values must increase in value as x increase in value.

3. provide a table of six values that does not represent a linear relation. All the y-values must be less than zero.

Thank You!

Sure, I'd be happy to help you with linear relations and creating tables and graphs.

1. To create a table of values that represent a linear relation where all the y-values are less than zero, we need to come up with a pattern or equation that describes a decreasing line. Let's use the equation y = -2x - 1 as an example.

First, choose six x-values that you can plug into the equation. Let's use -3, -2, -1, 0, 1, and 2.

Now, substitute each of these x-values into the equation to find the corresponding y-values.

For -3, y = -2(-3) - 1 = 5
For -2, y = -2(-2) - 1 = 3
For -1, y = -2(-1) - 1 = 1
For 0, y = -2(0) - 1 = -1
For 1, y = -2(1) - 1 = -3
For 2, y = -2(2) - 1 = -5

So, the table of values representing this linear relation is:

x | y
---------
-3 | 5
-2 | 3
-1 | 1
0 | -1
1 | -3
2 | -5

2. To create a table of values that does not represent a linear relation where all the y-values increase as x increases, we need to come up with a pattern or equation that describes a nonlinear relationship. Let's use the equation y = x^2 as an example.

Similarly, choose six x-values such as -3, -2, -1, 0, 1, and 2.

Now, substitute each of these x-values into the equation to find the corresponding y-values:

For -3, y = (-3)^2 = 9
For -2, y = (-2)^2 = 4
For -1, y = (-1)^2 = 1
For 0, y = (0)^2 = 0
For 1, y = (1)^2 = 1
For 2, y = (2)^2 = 4

So, the table of values representing this nonlinear relation is:

x | y
---------
-3 | 9
-2 | 4
-1 | 1
0 | 0
1 | 1
2 | 4

3. To create a table of values that does not represent a linear relation and where all the y-values are less than zero, we can use a different nonlinear equation as an example. Let's use the equation y = -x^2 - 1.

Choose six different x-values, such as -3, -2, -1, 0, 1, and 2.

Now, substitute each of these x-values into the equation to find the corresponding y-values:

For -3, y = -(-3)^2 - 1 = -8
For -2, y = -(-2)^2 - 1 = -3
For -1, y = -(-1)^2 - 1 = -2
For 0, y = -(0)^2 - 1 = -1
For 1, y = -(1)^2 - 1 = -2
For 2, y = -(2)^2 - 1 = -5

So, the table of values representing this nonlinear relation is:

x | y
---------
-3 | -8
-2 | -3
-1 | -2
0 | -1
1 | -2
2 | -5

I hope this helps you understand how to create tables for linear and nonlinear relations!