Question Video: Sketching the Graph of a Linear Relation 𝑎𝑥 + 𝑏𝑦 = c Given Values for the Coefficients 𝑎, 𝑏, and 𝑐 Mathematics • Second Year of Preparatory School

Video Transcript

Given the relation 𝑎𝑥 plus 𝑏𝑦 is equal to 𝑐, sketch its graph if 𝑎 is equal to zero, 𝑏 is three, and 𝑐 is equal to two.

To sketch the graph of 𝑎𝑥 plus 𝑏𝑦 is equal to 𝑐, where the coefficients take the values given, we first substitute these values into the equation. So, with 𝑎 equal to zero, 𝑏 equal to three, and 𝑐 equal to two, we have zero times 𝑥 plus three times 𝑦 is equal to two. That is, three 𝑦 is equal to two. And dividing through by three, this gives us 𝑦 is equal to two over three.

Before sketching this, let’s note that another way of looking at this is that in the linear relation 𝑎𝑥 plus 𝑏𝑦 is equal to 𝑐, if 𝑎 is equal to zero, the relation becomes 𝑦 is equal to 𝑐 over 𝑏. In the given problem, we have 𝑐 equal to two and 𝑏 equal to three. And as we found, 𝑦 is equal to two over three. To sketch the graph of this relation 𝑦 is equal to two over three, we note that the interpretation of this relation is that for every value of 𝑥, 𝑦 is equal to the constant value two over three. The graph of this relation then is a horizontal line through the point on the 𝑦-axis where 𝑦 is equal to two over three.