### Video Transcript

The scores of a class of students in their end-of-year math and physics examinations can be described by the model ๐ฆ equals 31.8 plus 0.43๐ฅ, where ๐ฅ is the score in math and ๐ฆ is the score in physics. What is the interpretation of the value of 0.43 in the model?

First, letโs imagine this model in the ๐ฅ๐ฆ-plane. We know you couldnโt have a negative physics score or a negative math score. And that means weโll just be dealing with the quadrant one result: when ๐ฅ is zero, ๐ฆ equals 31.8. And weโre dealing with a positive slope, where the math score, on average, is the ๐ฅ-axis and the physics score, on average, is the ๐ฆ-axis.

If we remember our form ๐ฆ equals ๐๐ฅ plus ๐, we know that the coefficient of ๐ฅ, the invariable, represents the slope and the constant ๐ represents the ๐ฆ-intercept. The slope is the changes in ๐ฆ over the changes in ๐ฅ. Related to our model, that would be the changes in physics scores over the changes in math scores. The invariable, the coefficient of ๐ฅ, in our problem would be 0.43. We could write that 0.43 as a fraction over one.

We could say as the math score increases by one point as we move to the right one place on our graph, the physics score will increase by 0.43. And so, we say for every additional point scored in the math examination, studentsโ scores increased by, on average, 0.43 additional points in their physics examination. And 0.43 is the relationship from the math score to the physics score.