Final answer:
The equation 5xy + 7x = 14 is non-linear because it includes the product of two different variables, x and y, which does not conform to the standard linear equation format y = mx + b or y = a + bx.
Step-by-step explanation:
The equation in question, 5xy + 7x = 14, is not a linear equation. Linear equations have variables that are to the first power only and do not have products of different variables. In contrast, the given equation includes a product of two variables, x and y, which indicates it's a non-linear equation.
The equation 5xy + 7x = 14 is a non-linear equation. A linear equation is an equation in which the highest power of the variable is 1. In this equation, the term 5xy has two variables, x and y, raised to the first power, but it is being multiplied together, which makes it a non-linear equation.
An example of a linear equation would be in the form of y = mx + b or y = a + bx, where m or b is the slope and a or b is the y-intercept. Therefore, the correct answer to whether the equation 5xy + 7x = 14 is linear or non-linear is 2) Non-linear.