What is the equation that holds true for x = 6 and x = 2?

To find an equation that is true for both x = 6 and x = 2, we can substitute these values into a general linear equation format, such as:

y = mx + b

Here, m is the slope and b is the y-intercept. The primary task is to determine if we can create an equation where both values satisfy the same output (y).

Let’s consider a basic approach. If we want y to have the same result for both values of x, we can choose a specific y-value to test. For instance, let’s say:

y = 0

Plugging in x = 6:

0 = m(6) + b

Which simplifies to:

b = -6m

Now, substituting x = 2:

0 = m(2) + b

This becomes:

0 = 2m - 6m

Which simplifies to:

4m = 0

This implies m = 0. Therefore, substituting back, we find that:

b = 0

Thus, the equation:

y = 0

is valid for both x = 6 and x = 2.

In conclusion, the equation that satisfies both conditions is a horizontal line, represented as:

y = 0

This shows that regardless of the value of x within this context, the output remains constant at 0. You could further explore other equations or forms such as quadratic or polynomial equations if you wish to introduce more complexity while exploring other results for these same x values.