What does the y-intercept represent in the equation y = 2x + 3?

The y-intercept represents the value of y when x is zero, which is 3 in this equation.

In the equation \( y = 2x + 3 \), the y-intercept is the point where the line crosses the y-axis. This occurs when the value of \( x \) is zero. To find the y-intercept, you simply substitute \( x = 0 \) into the equation. When you do this, the equation becomes \( y = 2(0) + 3 \), which simplifies to \( y = 3 \). Therefore, the y-intercept is 3.

The y-intercept is an important feature of a linear equation because it gives you a starting point for graphing the line. In this case, the line will cross the y-axis at the point (0, 3). This means that no matter what the value of \( x \) is, the line will always pass through this point when \( x \) is zero.

Understanding the y-intercept can also help you interpret real-world situations. For example, if the equation represented a relationship between time and distance, the y-intercept would tell you the initial distance when time is zero. In this way, the y-intercept provides valuable information about the starting condition of the relationship described by the equation.

In summary, the y-intercept in the equation \( y = 2x + 3 \) is 3, and it tells you where the line crosses the y-axis, providing a crucial point for graphing and understanding the linear relationship.