Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Which of the following is the slope-intercept form of a linear equation?

1. y = mx + b

2. Ax + By = C

3. y - y₁ = m(x - x₁)

4. y = k/x

The correct answer is: y = mx + b

The slope-intercept form of a linear equation is represented by the equation y = mx + b. In this equation, 'm' signifies the slope of the line, which indicates how steep the line is and the direction it takes as it moves across the Cartesian plane; a positive slope shows an upward movement, while a negative slope shows a downward movement. The 'b' represents the y-intercept, which is the point at which the line crosses the y-axis. This form is particularly useful because it provides a clear way to identify both the slope and the y-intercept at a glance, making it easy to graph the linear equation. In contrast, other forms such as Ax + By = C represent a standard form of a linear equation, which does not explicitly display the slope and y-intercept. The equation y - y₁ = m(x - x₁) is known as the point-slope form, primarily used when you have a specific point on the line and the slope but doesn't indicate the y-intercept directly. The equation y = k/x describes a hyperbola and is not linear at all, as it involves a variable in the denominator, ultimately producing a curve rather than a straight line. Thus, the first option is