### Video Transcript

Given the relation ππ₯ plus ππ¦
is equal to π, sketch its graph if π is equal to zero, π is three, and π is
equal to two.

To sketch the graph of ππ₯ plus
ππ¦ is equal to π, where the coefficients take the values given, we first
substitute these values into the equation. So, with π equal to zero, π equal
to three, and π equal to two, we have zero times π₯ plus three times π¦ is equal to
two. That is, three π¦ is equal to
two. And dividing through by three, this
gives us π¦ is equal to two over three.

Before sketching this, letβs note
that another way of looking at this is that in the linear relation ππ₯ plus ππ¦ is
equal to π, if π is equal to zero, the relation becomes π¦ is equal to π over
π. In the given problem, we have π
equal to two and π equal to three. And as we found, π¦ is equal to two
over three. To sketch the graph of this
relation π¦ is equal to two over three, we note that the interpretation of this
relation is that for every value of π₯, π¦ is equal to the constant value two over
three. The graph of this relation then is
a horizontal line through the point on the π¦-axis where π¦ is equal to two over
three.