Ohio Assessments for Educators (OAE) Mathematics Practice Exam

How is the point-slope form of a line expressed?

1. y = mx + b

2. y - y₁ = m(x - x₁)

3. Ax + By = C

4. x/x₁ + y/y₁ = 1

The correct answer is: y - y₁ = m(x - x₁)

The point-slope form of a line is expressed as y - y₁ = m(x - x₁), where (x₁, y₁) represents a specific point on the line, and m represents the slope of the line. This format is particularly useful for writing the equation of a line when you know one point on the line and the slope. In this form, the expression y - y₁ signifies the vertical distance from the known point (x₁, y₁) to any point (x, y) on the line. The right side, m(x - x₁), describes how the line's slope m changes horizontally from the point (x₁, y₁). Thus, this form directly relates any point on the line to a known point and provides a clear relationship between x and y based on the slope. Understanding this concept is essential for graphing lines or for determining the equation of a line given a point and a slope, making this form particularly versatile and widely used in algebra and coordinate geometry.