Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

In the equation for a straight line, what does 'b' represent?

1. The slope of the line

2. The angle of the line

3. The y-intercept

4. The x-intercept

The correct answer is: The y-intercept

In the equation of a straight line, commonly expressed in the slope-intercept form \(y = mx + b\), 'b' represents the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, which occurs when the value of x is zero. At this point, the y-coordinate, or the output of the equation when x is substituted with zero, is exactly 'b'. Understanding the role of the y-intercept is crucial in graphing linear equations, as it gives a clear starting point for plotting the line on the coordinate plane. While the slope, indicated by 'm', describes how steep the line is and the direction it goes (up or down), the y-intercept is essential in determining the vertical position of the line on the graph. This foundational concept is key to interpreting and working with linear equations effectively.