Question

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.

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