Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What does 'b' in the slope-intercept form indicate?

1. The slope of the line

2. The x-intercept of the line

3. The y-intercept of the line

4. The coefficient of x

The correct answer is: The y-intercept of the line

In the slope-intercept form of a linear equation, which is represented as \( y = mx + b \), the term 'b' specifically indicates 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. This means that if you substitute zero for x in the equation, the resulting value of y will equal b. Understanding the position of the y-intercept is crucial for graphing linear equations, as it provides a starting point on the coordinate plane. The slope, represented by 'm', describes how steep the line is and the direction it moves with respect to the x-value, but it is the 'b' value that definitively tells where the line intersects the y-axis. This central role of 'b' in determining the y-intercept distinguishes it from other elements of the equation, further emphasizing its importance in graphing and understanding linear functions.