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


25=x2+y2



(y+7)=3(x−2)

Answer 1

Let's analyze the mathematical expressions provided one by one:

1. \(25 = x^2 + y^2\)

   • Type: This is a nonlinear equation because it represents a circle (specifically, a circle with radius 5 centered at the origin).
   • Function: This is not a function because for some values of \(x\), there are two corresponding values of \(y\) (one positive and one negative).

2. \((y + 7) = 3(x - 2)\)

   • Type: This is a linear equation in the form of \(y = mx + b\). It can be rewritten as \(y = 3x - 6\).
   • Function: This is a function because for every \(x\) value, there is exactly one \(y\) value.

Summary:

| Expression | Linear | Nonlinear | Function | Not a Function | |-------------------------------------|--------------|-----------|-----------|-----------------| | \(25 = x^2 + y^2\) | | Nonlinear | | Not a Function | | \((y + 7) = 3(x - 2)\) | Linear | | Function | |