What are the coordinates for the equations x = 8 and y = -8?

Understand the Problem

The question involves filling in coordinates for the equations x = 8 and y = -8, likely requiring an understanding of how these equations define lines in a coordinate plane.

Answer

For $x = 8$: $(8, 0), (8, 1), (8, -3), (8, 5)$ For $y = -8$: $(2, -8), (5, -8), (10, -8), (15, -8)$

Steps to Solve

Understand the equations
The equation $x = 8$ means that for each point on this line, the x-coordinate is fixed at 8, while the y-coordinate can be any real number.
For the equation $y = -8$, the y-coordinate is fixed at -8, while the x-coordinate can be any real number.
Identify the coordinates for $x = 8$
For $x = 8$, the coordinates can be represented as $(8, y)$, where $y$ can be any value.
Example coordinates:

For $y = 0$: $(8, 0)$
For $y = 1$: $(8, 1)$
For $y = -3$: $(8, -3)$
These will fill the table.

Identify the coordinates for $y = -8$
For $y = -8$, the coordinates can be represented as $(x, -8)$, where $x$ can be any value.
Example coordinates:

For $x = 2$: $(2, -8)$
For $x = 5$: $(5, -8)$
For $x = 10$: $(10, -8)$
These will fill the table as well.

For the lines you can fill in the answers as follows:

For $x = 8$ you can write:

$(8, 0)$
$(8, 1)$
$(8, -3)$
$(8, 5)$

For $y = -8$ you can write:

$(2, -8)$
$(5, -8)$
$(10, -8)$
$(15, -8)$

More Information

The equations represent vertical and horizontal lines on a coordinate plane. The line $x = 8$ is a vertical line at x = 8, while the line $y = -8$ is a horizontal line at y = -8. This means that any combination of the other coordinate values will still be valid as long as the specified constant is adhered to.

Tips

Using wrong coordinates: Ensure that for $x = 8$, the x-coordinate is always 8, and similarly for $y = -8$, the y-coordinate should be -8.
Mixing up the roles of x and y: It’s important to remember which variable is being held constant in each equation.

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