Determine if the function defined by each of the equations listed below is either linear or non-linear. Drag each equation on the left to the correct determination on the right.

Question

Choices
3x 2^ - 2y=4 y=4+3x y=x 3^ -5 4x-3y=2 -5x 2^+y=3
Answers

linear
not linear

Answer 1

Let's analyze each equation to determine if it is linear or non-linear.

1. 3x - 2y = 4

   • This equation can be rearranged into the form y = mx + b (the slope-intercept form).
   • Rearranging gives:
     \( 2y = 3x - 4 \)
     \( y = \frac{3}{2}x - 2 \)
   • Conclusion: linear

2. y = 4 + 3x

   • This is already in slope-intercept form (y = mx + b).
   • Here, the slope (m) is 3 and the y-intercept (b) is 4.
   • Conclusion: linear

3. y = x^3 - 5

   • This equation involves x raised to the power of 3, which is not a linear term.
   • Conclusion: not linear

4. 4x - 3y = 2

   • This equation can also be rearranged into the form y = mx + b.
   • Rearranging gives:
     \( 3y = 4x - 2 \)
     \( y = \frac{4}{3}x - \frac{2}{3} \)
   • Conclusion: linear

5. -5x^2 + y = 3

   • This equation involves x raised to the power of 2, indicating it is a quadratic function.
   • Conclusion: not linear

Now, let's sort the equations based on the determinations:

Linear:

• 3x - 2y = 4
• y = 4 + 3x
• 4x - 3y = 2

Not Linear:

• y = x^3 - 5
• -5x^2 + y = 3