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?

  • If these points are connected, they will form a straight line:
    • The graph of a linear relationship is a straight line which can be defined by two  points that lie in the same plane.
    • Linear relationships can be represented in tables, graphs, situations (such as a growth pattern), and equations.
    • The slope and y-intercept and be identified in each of the representations stated above.
  • Examples of lines and non-lines are shown below.
Examples of Lines

Examples of Non-Lines

  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 in \(y\) (which is the rise) and change in \(x\) (which is the run).
  • The change in a value is denoted by the symbol \(delta \Delta\)

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

  • The slope can be found in graphed linear relationships by determining the rise and the run between any two 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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