y = x + 6
The given equation is y = x + 6
The given equation is y = x + 6. This is a linear equation in two variables, x and y.
In this equation, for every value of x, we can determine the corresponding value of y by adding 6 to x.
For example:
– When x = 0, y = 0 + 6 = 6
– When x = 2, y = 2 + 6 = 8
– When x = -4, y = -4 + 6 = 2
We can also express this equation in the form of a table to easily find the values of x and y:
| x | y |
|—|—|
| 0 | 6 |
| 2 | 8 |
| -4| 2 |
We can plot these points on a graph, where the x-values are represented on the x-axis and the y-values on the y-axis. After plotting the points, we can draw a straight line passing through these points. This line represents all the possible solutions of the equation y = x + 6.
In this case, the line has a positive slope of 1, which means that for every increase of 1 in x, y will also increase by 1. The intercept on the y-axis is 6, indicating that when x = 0, y = 6.
This equation can also be used in problem-solving situations, where we can substitute values of x and solve for y or vice versa.
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