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 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.
- 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: \(s(n)=3n+1\)