Classify each equation as defining �yy as a linear or nonlinear function of �xx. Select one cell per column.​

Question

�
=
7
×
4
�
y=7×4x
�
=
(
2
�
+
5
)
2
y=(2x+5)
2

�
=
10
�
2
y=10x
2

�
=
5
�
−
3
y=5x−3
�
=
�
2
y=
2
x
​

�
=
2
�
3
+
1
y=2x
3
+1
linear

nonlinear

Answer 1

Let's classify each equation as either defining \( y \) as a linear or nonlinear function of \( x \):

1. \( y = 7 \times 4x \)

   • Linear (can be simplified to \( y = 28x \))

2. \( y = (2x + 5)^2 \)

   • Nonlinear (it is a quadratic function)

3. \( y = 10x^2 \)

   • Nonlinear (it is a quadratic function)

4. \( y = 5x - 3 \)

   • Linear (it is a linear equation)

5. \( y = 2x \)

   • Linear (it is a linear equation)

6. \( y = 2x^3 + 1 \)

   • Nonlinear (it is a polynomial function of degree 3)

Here’s the classification:

| Equation | Linear/Nonlinear | |------------------------------|------------------| | \( y = 7 \times 4x \) | Linear | | \( y = (2x + 5)^2 \) | Nonlinear | | \( y = 10x^2 \) | Nonlinear | | \( y = 5x - 3 \) | Linear | | \( y = 2x \) | Linear | | \( y = 2x^3 + 1 \) | Nonlinear |