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


=
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

1 answer

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 |