The equation \(2x + 3y = 39\) is a linear equation.
Here's why:
-
Linear: A linear equation is one that can be expressed in the form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are constants. In this case, \(A = 2\), \(B = 3\), and \(C = 39\), so it fits this form.
-
Function: This equation can be rearranged to find \(y\) in terms of \(x\): \[ 3y = 39 - 2x \implies y = \frac{39 - 2x}{3} \implies y = -\frac{2}{3}x + 13. \] This shows that \(y\) is a function of \(x\) (specifically, a linear function).
Therefore, \(2x + 3y = 39\) is a linear function.