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 in
  2. Are these patterns linear relationships?
  • Yes. The plotted points from Patterns 2, 3, and 4 are linear.  

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

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

  1. Compute the slope for the remaining patterns using the graphs.
  • The slope from Pattern 2 is \(\frac{2}{1}=2\).
  • The slope from Pattern 3 is \(\frac{3}{1}=3\).
  • The slope from Pattern 4 is \(\frac{3}{1}=3\).

Go to Making Connections (Tables)