Question

is the equation linear? explain
7x+3y=21
the equation is linear because both of the variables in the equation have an exponent that is positive
the equation is linear because both of the variables in the equation have an exponent of 1.
the equation is not linear because a, b, and c are all positive constants, and neither a nor b is zero.
the equation is not linear because c is equal to ab.

Explanation:

A linear equation in two variables is of the form \(Ax + By = C\) where \(A\), \(B\), and \(C\) are constants, and the exponents of \(x\) and \(y\) are 1. For the equation \(7x + 3y = 21\), the exponents of \(x\) and \(y\) are both 1. The first option's reasoning (exponent positive) is incorrect as linearity requires exponent 1, not just positive. The third and fourth options are incorrect as the equation meets the linear equation criteria. So the correct reasoning is that the equation is linear because both variables have an exponent of 1.

Answer:

The equation is linear because both of the variables in the equation have an exponent of 1.