Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the standard form of a line equation?

1. y = mx + b

2. Ax + By = C

3. y - y₁ = m(x - x₁)

4. y - y₂ = m(x - x₂)

The correct answer is: Ax + By = C

The standard form of a line equation is expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This format is widely used in algebra because it allows for easier manipulation of linear equations, especially when determining intercepts and analyzing multiple lines in relation to each other. In standard form, the coefficients A and B give immediate insight into the slope of the line when rearranged, but this format also provides a clear visual representation of how the line interacts with the axes. The equation can be used to derive other forms of the linear equation, such as slope-intercept form and point-slope form, which may help in solving for specific values or understanding the characteristics of the line. The other forms presented, although valid equations of a line, serve different purposes. For instance, y = mx + b is the slope-intercept form, which explicitly defines the slope and y-intercept. The point-slope form (y - y₁ = m(x - x₁)) focuses on a specific point on the line and the slope, which is particularly useful for graphing or finding the equation given a point and a slope.