Question

True or false: An equation in the form of Ax + By = C, where A > 0, A and B are not both zero, and A, B, and C are integers with a greatest common factor of 1 can represent either a linear or nonlinear function. O True O False

Answer 1

The equation Ax + By = C represents a linear equation, since both x and y have exponents 1. We can also write this equation in the slope-intercept form:

`\begin{gathered} Ax+By=C \\ By=-Ax+C \\ y=-(A)/(B)x+(C)/(B) \end{gathered}`

So the slope of the linear equation is -A/B and the y-intercept is C/B.

This equation cannot represent a nonlinear function, therefore the correct option is FALSE.