Understand that a two-variable equation's graph is the set of all ordered-pair solutions.
Generate ordered-pair solutions from input values
Problem
Calculate the ordered-pair solutions for \(y~=~2x~+~1\) at \(x~=~-1,~0,~\text{and}~2\).
Big Picture
What this problem is really about
The equation acts as one input-output rule for all three supplied inputs. We’ll substitute each input separately, use parentheses around the negative value to protect its sign, and keep the constant term in every calculation. Each computed output is then paired with the input in x-then-y order, and the graph provides a visual check that all resulting points lie on the same line.
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