For each table, graph and equation, select whether it is linear and whether it is a function.(6 points) Linear Nonlinear Function Not a Function (y+7)=3(x−2) 25=x2+y2 Skip to navigation

Answer 1

To determine whether the equations are linear or nonlinear and whether they represent functions, let's analyze each item given:

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

   • Linear or Nonlinear: This equation can be rearranged to the format \(y = mx + b\). Specifically, it rearranges to \(y = 3x - 6 - 7\) or \(y = 3x - 13\). Thus, it is a linear equation.
   • Function or Not a Function: This represents a function because for each x-value, there is exactly one corresponding y-value.
   • Conclusion: Linear, Function.

2. Equation: 25 = x² + y²

   • Linear or Nonlinear: This is an equation of a circle with radius 5 (as it can be rearranged to \(x² + y² = 25\)). Since it cannot be written in the form \(y = mx + b\), it is nonlinear.
   • Function or Not a Function: This equation does not represent a function because it does not pass the vertical line test (i.e., for some x-values, there are multiple y-values).
   • Conclusion: Nonlinear, Not a Function.

In summary:

1. (y + 7) = 3(x - 2) → Linear, Function.
2. 25 = x² + y² → Nonlinear, Not a Function.