Question

Which statement best explains whether y = 3x + 5 is a linear function or a nonlinear function?

help

Answer 1

Any linear function has the form y = mx + b and there is NO exponent on the x. So you are looking for yes answers to these two questions:

1) Is y a function of x?

2) Is there no exponent but x present?

1) Has a yes answer as y = ________ puts the equation in function form. The exponent is 1, (x to the first). Thus, y = 3x+5 is a linear function because its exponent is one and it's expressed as a function.

Answer 2

y = 3x + 5 is a linear function because the exponent of x is 1.

In a line formula, the biggest exponent of x in standard form represents how many times the line changed direction.

For example if the equation was y = 4x + 4x^4 + 5 - 2x^2 + 6x^3 (I know it's a long one), then the line changed direction 4 times because the biggest exponent of x is 4.

Or we can use it vice versa, which would be "If the graph changed direction 4 times..." or they gave you a graph and line changes direction 4 times; then the equation has to have a maximum x exponent of 4.

In this case, we have an exponent of 1 which makes the line a straight one. And we call straight lines on a graph "linear".