Which of the following equations represents a linear function?

A linear function is defined by an equation that can be represented in the form ( y = mx + b ), where ( m ) and ( b ) are constants, and ( m ) represents the slope of the line, while ( b ) indicates the y-intercept.

The equation ( y = 2x + 3 ) perfectly fits this form. Here, the slope ( m = 2 ) indicates that for every one unit increase in ( x ), ( y ) increases by two units, and the y-intercept ( b = 3 ) tells us that the line crosses the y-axis at ( (0, 3) ). This demonstrates a constant rate of change, which is a key characteristic of linear functions.

In contrast, the other equations represent different types of relationships:

• The equation ( x^2 + y^2 = 1 ) describes a circle, not a linear function, as it involves squared terms.

• The equation ( xy = 5 ) depicts a hyperbola, which also shows a non-linear relationship because ( y ) is implicitly defined in terms of ( x ) and involves multiplicative interaction.

• Lastly, the equation