Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

How do you determine the slope of a line from its equation?

1. By identifying the y-intercept in the equation

2. By extracting the constant from the equation

3. By identifying the coefficient of x in the slope-intercept form

4. By calculating the distance between two points

The correct answer is: By identifying the coefficient of x in the slope-intercept form

To determine the slope of a line from its equation, identifying the coefficient of x in the slope-intercept form is the essential step. The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b represents the y-intercept. Here, the coefficient of x (which is m) directly gives the slope of the line. Understanding this form allows one to quickly and easily assess the slope without needing to convert the equation from another form, such as standard form. While the y-intercept is important for graphing, it does not provide information about the steepness or direction of the line, which is encapsulated in the slope. The other methods mentioned, such as extracting a constant or calculating distances between points, do not directly yield the slope from an equation. Hence, focusing on the coefficient of x in the slope-intercept form is the most effective way to determine the slope of the line.