Complete each section to show your understanding for linear patterns.
The following tables represent linear patterns. The tables are created using Desmos.com.
- Find the missing values in each table.
- Graph each table on an \(x\)-\(y\) coordinate plane.
- Calculate the slope using the table.
- Calculate the slope using the graph.
- Determine the point of the \(y\)–intercept
- Write an equation to determine the \(y\)–value given any \(x\)-value.
Given the growth pattern shown in Figure 2 and Figure 4.
- Draw Figure 3.
- Explain the growth pattern.
- Determine the number of squares in Figure 0.
- Write the equation to represent the number of squares for any figure.
- Using the context of growth patterns, explain why \(m\) represents the slope and \(b\) represents the \(y\)-intercept in the slope-intercept formula \(y=mx+b\).
A given linear pattern has 10 squares in Step 3. The pattern grows by -4 squares every 2 steps.
- Create a table for this pattern.
- Calculate the slope to represent the growth for this pattern.
- Calculate the equation to calculate the number of squares for each step.