Question Video: Sketching the Graph of a Linear Relation given the Coefficients Mathematics • Second Year of Preparatory School

Video Transcript

Given the relation 𝑎𝑥 plus 𝑏𝑦 equals 𝑐, sketch the graph of this relation if 𝑎 equals five, 𝑏 equals zero, and 𝑐 equals one.

To sketch the graph of the given relation, we first substitute the given values for the coefficients 𝑎, 𝑏, and 𝑐 into the equation. This gives five times 𝑥 plus zero times 𝑦 equals one. That is, five 𝑥 equals one. And we can make 𝑥 the subject of this new equation by dividing through by five, so we have 𝑥 is equal to one-fifth.

We could look at this another way by recalling that if 𝑏 equals zero in the linear relation 𝑎𝑥 plus 𝑏𝑦 equals 𝑐, then 𝑥 is equal to 𝑐 over 𝑎. And this is exactly what we found with 𝑐 equal to one and 𝑎 equal to five.

Now to sketch the graph of this relation, 𝑥 equals one-fifth, we note that this relation is interpreted as “For every value of 𝑦, 𝑥 is equal to one-fifth.” The graph of this relation is therefore a vertical line through 𝑥 equals one-fifth, which we note as a decimal is 0.2. Hence, the graph of the relation 𝑎𝑥 plus 𝑏𝑦 equals 𝑐 with 𝑎 equals five, 𝑏 equals zero, and 𝑐 equals one is a vertical line through 𝑥 equals 0.2.