For each table, graph and equation, select whether it is linear and whether it is a function.(6 points)

Question

Linear Nonlinear Function Not a Function






(y+7)=3(x−2)

25=x2+y2



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Answer 1

To determine whether each equation is linear or nonlinear and whether it is a function or not, we can analyze each one step by step.

1. Equation: (y + 7) = 3(x - 2)

   • Linear/Nonlinear: This is a linear equation because it can be rewritten in the form \(y = mx + b\). Rearranging gives us \(y = 3x - 6 - 7\) or \(y = 3x - 13\).
   • Function/Not a Function: This is a function because for each x-value there is exactly one y-value.

2. Equation: 25 = x² + y²

   • Linear/Nonlinear: This is a nonlinear equation because it describes a circle (implicit form), which is not a straight line.
   • Function/Not a Function: This is not a function because for some x-values, there are two corresponding y-values (one positive and one negative).

Here’s how you can summarize this information:

| Equation | Linear | Nonlinear | Function | Not a Function | |---------------------------------|----------------|----------------|--------------------|---------------------| | (y + 7) = 3(x - 2) | Yes | | Yes | | | 25 = x² + y² | | Yes | | Yes |

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