LINR 1 | Lesson 1 | Making Connections (Graphed Points)

Making Connections

Graphed Points

The graphed points from Pattern 1 are shown below where the \(x\)-value represents the step and the \(y\)value represents the number of squares in that step.

Pattern 1

What do you notice about the pattern of these points?

  • The points are collinear {a set of points lying in the same straight line)
  • Linear relationships can be represented in tables, graphs, situations (such as a growth pattern), and equations.
  • The rate of change (slope) can be identified in linear relationships.
  1. Use the table from each pattern to graph the points for Patterns 2, 3, and 4.
  2. Are these patterns linear relationships?

How can you use the graphed points to find the slope?

  • Slope is the rate of change of a linear function and is a measure of the steepness of a line using the change in \(y\) (which is the rise) and change in \(x\) (which is the run).
  • The change in a value is denoted by the symbol \(delta \Delta\)

\[slope=\frac{\text {change in } y}{\text{change in }x}=\frac{\Delta y}{\Delta x} =\frac {rise}{run}\]

  • The slope can be found in graphed linear relationships by determining the rise and the run between any two collinear points.
  • The rise and the run for Pattern 1 is shown on the graph below. Graphs are created using Desmos.com.

\[slope=\frac{\Delta y}{\Delta x} =\frac {rise}{run}=\frac {+2}{+1}=2\]

  1. Compute the slope for the remaining patterns using the graphs.

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