Looking at the fifth row:
1.
5xy = 2: This equation contains the term xy (product of x and y), which makes it nonlinear. It represents a hyperbola.
2.
y + x = 4x + 5: This can be simplified to y = 3x + 5, which is in the form y = mx + b. This is linear.
3.
y = 3x + x²: This contains an x² term, making it a quadratic equation. This is nonlinear.
4.
Graph: This appears to be a cubic function (or similar polynomial) with an S-shape, which is clearly nonlinear.
Now I have analyzed all items in the grid. Let me compile my findings to provide a complete answer.
Linear Equations/Graphs:
- Yards to Feet (graph)
- Third graph (straight line)
- y = x + 5
- 4x/3 (interpreted as y = 4x/3)
- y = 4.7
- y = πx
- 2x + 3y = 7
- y = 4(x-1)
- 5y = 2x
- y = (2/5)x
- 10y = 4x
- y + x = 4x + 5
Nonlinear Equations/Graphs:
- Yards to Square Yards (graph)
- Fourth graph (parabola)
- First graph in second row (sideways parabola)
- y = 1 - x²
- y = 4/x
- 5xy = 2
- y = 3x + x²
- Last graph (cubic-like curve)
The solution involves categorizing each item based on whether it represents a linear relationship (straight line graph or equation that can be written in the form y = mx + b or Ax + By = C) or a nonlinear relationship (curved graph or equation containing terms like x², 1/x, xy, etc.).
Parent Tip: Review the logic above to help your child master the concept of linear and nonlinear functions worksheet.
