Question

7-14 Determine whether the equation or table defines y as a function of x.

\({\bf{3}}x - {\bf{5}}y = {\bf{7}}\)

Short answer

The equation defines y as a function of x.

Step-by-step solution

Simplify the given equation

Subtract \(3x\) on both sides of the equation \(3x - 5y = 7\).

\(3x - 5y - 3x = 7 - 3x\)

\( - 5y = 7 - 3x\)

Simplify the given equation

Multiply the equation \( - 5y = 7 - 3x\) by \( - \frac{1}{5}\).

\(y = - \frac{7}{5} + \frac{3}{5}x\)

\( = \frac{1}{5}\left( {3x - 7} \right)\)

From the above equation, for one value of x, there is only one value of y.

So, the given equation defines y as a function of x.