Determine if each function is linear or nonlinear.

Question

Drag each function into a box to correctly classify it.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
linear nonlinear
13y=13x+5
y=x+255
y³ = x
3y = x²
y=x2−19

Answer the question, sorting them out one by one

Answer 1

Let's classify each of the given functions as either linear or nonlinear:

1. 13y = 13x + 5

   • This can be rewritten as \( y = x + \frac{5}{13} \). It is in the form \( y = mx + b \) (where \( m \) is the slope and \( b \) is the y-intercept), so it is linear.

2. y = x + 255

   • This is already in the form \( y = mx + b \). It is a linear function since it can be written as \( y = 1x + 255 \). It is linear.

3. y³ = x

   • This can be rewritten as \( y = x^{1/3} \). This is not in the form \( y = mx + b \) and involves a cubic term on \( y \), so it is nonlinear.

4. 3y = x²

   • This can be rewritten as \( y = \frac{1}{3} x² \). Since it involves a squared term of \( x \), it is nonlinear.

5. y = x² - 19

   • This is a quadratic function in its standard form. It is not linear because it contains a squared term, so it is nonlinear.

Now, here's the classification:

Linear:

• 13y = 13x + 5
• y = x + 255

Nonlinear:

• y³ = x
• 3y = x²
• y = x² - 19

You can place the functions into the respective boxes accordingly.