Learning Targets

1.05B - I can describe and sketch linear, quadratic, and inverse patterns and identify similarities and differences. (more about hand-drawing/identifying with real data on graphs)
1.06A - I can interpret linear mathematical models, including the meaning of slope, y-intercept, and individual points.
1.06B - I can interpret inverse or quadratic mathematical models, including the meaning of slope, y-intercept, and individual points.
1.06C - I can interpret any mathematical model, including the meaning of slope, y-intercept, and individual points.
1.07C - I can take a set of data and represent on a graph with the correct model.  I can follow the conventions for creating a graph and include error bars.

Can you...

  • Use Logger Pro software to perform graphical analysis of data.
  • Make test plots of data to find linear relationships
  • Write mathematical models, in standard y = mx + b form, for linearized data. Replace m and b with constants including units and replace y and x with dependent and independent variable names.
  • Provide interpretations for the physical significance of the slope and y-intercept.
  • Relate mathematical and graphical expressions
  • Use proportional reasoning in problem solving

Interpreting Graphs

  • Points:(x,y) => (I.V., D.V.) A point will ALWAYS give us a prediction of our dependent variable for a specific independent variable value
  • Slope: Slope ALWAYS tells us specifically how the dependent variable changes (increases/decreases) as we increase the independent variable,  but this relationship might not always be constant
  • Y-intercept: The y-intercept ALWAYS tells us about the dependent variable when our independent variable is ZERO
  • ​Conclusion: SLOPE is the difference​

Graphical Models

Linear
  • Points:(x,y) => (I.V., D.V.) A point will give us a prediction of our dependent variable for a specific independent variable value
  • Slope: Slope tells us specifically how the dependent variable changes (increases/decreases) as we increase the independent variable. BUT it looks like the slope is different at different places…
  • Y-intercept: The y-intercept tells us about the dependent variable when our independent variable is ZERO
Quadratic
  • Points:(x,y) => (I.V., D.V.) A point will give us a prediction of our dependent variable for a specific independent variable value
  • Slope: Slope tells us specifically how the dependent variable changes (increases/decreases) as we increase the independent variable. BUT it looks like the slope is different at different places…
  • Y-intercept: The y-intercept tells us about the dependent variable when our independent variable is ZERO​
Inverse
  • Points:(x,y) => (I.V., D.V.) A point will give us a prediction of our dependent variable for a specific independent variable value
  • Slope: Slope tells us specifically how the dependent variable changes (increases/decreases) as we increase the independent variable. BUT it looks like the slope is different at different places…
  • Y-intercept: The y-intercept tells us about the dependent variable when our independent variable is ZERO. BUT this looks like it might not cross the y-axis…
Flat-line
  • Points:(x,y) => (I.V., D.V.) A point will give us a prediction of our dependent variable for a specific independent variable value
  • Slope: Slope tells us specifically how the dependent variable changes (increases/decreases) as we increase the independent variable. BUT it looks like the slope is zero…
  • Y-intercept: The y-intercept tells us about the dependent variable when our independent variable is ZERO

Determining Fit