College Math CLEP Prep Practice Exam

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What does the equation 3x + 2y = 6 represent?

A circle
A line
A hyperbola
An ellipse

The correct answer is: A line

3x + 2y = 6 is a linear equation, meaning it represents a line on a graph. This is because the variables x and y are raised to the first power and there are no other terms such as x^2 or y^2 present. A circle, hyperbola, and ellipse all have equations with higher powers, making them non-linear. Therefore, options A, C, and D are incorrect. Additionally, the equation of a circle, (x-h)^2 + (y-k)^2 = r^2, has x and y terms both squared, while a hyperbola and ellipse have a difference in signs between the terms being squared.