Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the general form equation that represents a line using intercepts?

1. Ax + By = C

2. y = mx + b

3. x/x₁ + y/y₁ = 1

4. y - y₁ = m(x - x₁)

The correct answer is: x/x₁ + y/y₁ = 1

The general form equation using intercepts is represented by the equation where the x-intercept is denoted as \( x_1 \) and the y-intercept as \( y_1 \). This format expresses a line in terms of where it intersects the x-axis and y-axis. Specifically, the equation \( \frac{x}{x_1} + \frac{y}{y_1} = 1 \) articulates that any point on the line can be represented as a combination of its intercepts. This format is particularly useful in identifying the intercepts directly from the equation: setting \( y = 0 \) solves for the x-intercept, while setting \( x = 0 \) solves for the y-intercept. Hence, it gives a direct geometric interpretation of the relationship between the variables. In practical applications, this form is beneficial for quickly determining how a line behaves in a Cartesian coordinate system, making it a preferred choice in certain contexts over the various standard forms. The other formats mentioned serve different purposes: one provides a slope-intercept perspective, another is a point-slope form, and the first one is the standard form of a linear equation. Each has its own significance but does not specifically combine the usage of