Scales to Graphs

Scales are representations of mathematical relationships.

A linear relationship can be represented by a table of x and y values, a graph, or a combination of linear scales.

An exponential or logarithmic relationship can also be represented by a table, a graph, or a logarithmic and linear scale.

Combined Linear and Logarithmic Scale

We will make a linear scale beneath a logarithmic scale. One unit on the linear scale will be the distance that represents multiplying by 2.

• Measure and record the distance between the locations of 1 and 2 on the logarithmic scale
• Create a linear scale
  • Start by locating the linear scale 0 in the same place as the 1 on the logarithmic scale
  • Mark and label a linear scale for the whole numbers up to the end of the logarithmic scale
  • Note that this scale lets you estimate y=2^x and x=\log_2 y, especially for values of x that are not a whole number