Do all linear equations have x intercepts?

No, not all linear equations have x-intercepts. An x-intercept is where a line crosses the x-axis, meaning the value of y is zero at that point.

For a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept, the x-intercept can be found by setting y to zero and solving for x:

Example: For the equation y = 2x + 4, setting y to zero gives:

0 = 2x + 4

Solving this, we get:

2x = -4

x = -2

So, this line intersects the x-axis at (-2, 0). Therefore, this particular linear equation does have an x-intercept.

However, consider the case of a vertical line represented by the equation x = k, where k is any constant. This line does not intersect the x-axis, as it runs parallel to it. In this case, there is no x-intercept.

In summary, while many linear equations do have x-intercepts, vertical lines do not, which means not all linear equations have x-intercepts.