Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the slope in the equation of a line given in the form y = mx + b?

1. m

2. b

3. y

4. x

The correct answer is: m

In the equation of a line represented in the slope-intercept form \( y = mx + b \), the letter \( m \) stands for the slope of the line. This form is particularly useful because it clearly distinguishes the slope from the y-intercept, which is denoted by \( b \). The slope \( m \) quantifies the rate at which \( y \) changes with respect to \( x \). Specifically, it indicates how much \( y \) increases or decreases as \( x \) increases by one unit. If \( m \) is positive, the line rises as it moves from left to right; if \( m \) is negative, the line falls. Understanding this relationship is crucial for graphing linear equations and for interpreting real-world situations modeled by linear relationships. On the other hand, \( b \) represents the y-intercept, which is the point where the line crosses the y-axis. The variables \( y \) and \( x \) represent the output and input of the function, respectively, but they are not indicative of the slope. Therefore, the answer correctly identifies \( m \) as the slope, affirming the role of this coefficient in defining the behavior of the linear equation.