LINR 1 | Lesson 1 | Making Connections (Equations)

Making Connections

Equations

How can you use the pattern’s equation to find the slope and the \(y\)-intercept?

  • The equation shows both the slope (growth rate) and the \(y\)-intercept which is the number of squares in Step \(0\). 

Use Pattern 1 below to determine the slope and \(y\)-intercept.

Pattern 1
  • Pattern 1 grows by 2 squares \(s(n)\) for every one step \(n\).
  • Pattern 1 has 4 squares at Step 0, which is the starting point or the \(y\)-intercept of \((0,4)\).
  • The equation for Pattern 1 is: \(s(n)=2n+4\), where \(n\) represents the step number and \(s(n)\) represents the number of squares at any given step \(n\).
  • The slope of 2 is the coefficient of \(n\) and the \(y\)-intercept \((0,4)\) is the constant. This equation gives the rule to start with 4 at Step \(0\) and add 2 for each step.
  1. Circle the slope and underline the \(y\)-intercept for the remaining pattern equations.

Pattern 2 Equation: \(s(n)=2n+1\) 

Pattern 3 Equation: \(s(n)=3n+2\)

Pattern 4 Equation: \(s(n)=3n+1\)


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