The slope of a linear function plays a crucial role in determining the number of zeros the function has. A linear function can be expressed in the form of y = mx + b, where m represents the slope and b is the y-intercept.
If the slope m is not equal to zero, the function will have exactly one zero, or x-intercept, which is the point at which the line crosses the x-axis. This is because as the value of x changes, the function will rise or fall continuously, ensuring it will intersect the x-axis at one point.
On the other hand, if the slope m is zero, the function simplifies to y = b, which is a horizontal line. In this case, the line does not cross the x-axis unless b is also zero. If b is zero, there are infinitely many zeros since every point on the x-axis is a zero. If b is not zero, the function has no zeros at all.
In summary, a linear function with a non-zero slope will always have one zero, while a function with a zero slope may have none or infinitely many, depending on the value of b.