The equation y = x + 1 represents a linear function, where for every value of x, there is a corresponding value of y. To find the solutions to this equation, we can rearrange it based on specific values of x.
Let’s explore how to find solutions:
- When x = 0:
Substitute x with 0:
y = 0 + 1
Therefore, y = 1.
So, one solution is (0, 1). - When x = 1:
Substitute x with 1:
y = 1 + 1
Thus, y = 2.
Another solution is (1, 2). - When x = -1:
Substitute x with -1:
y = -1 + 1
As a result, y = 0.
This gives us the solution (-1, 0).
In general, any point of the form (x, x + 1) is a solution to the equation. Therefore, different values of x can yield infinite solutions. Just remember that the linear equation forms a straight line on a graph, meaning there are countless solutions along this line!
In summary, the solutions to the equation y = x + 1 can be expressed as pairs of (x, y) coordinates, such as (0, 1), (1, 2), and (-1, 0). You can choose any real number for x to find a corresponding y.