Understand graphs of equations

What you'll learn

1. Explain that the graph of an equation in two variables is the set of ALL ordered pairs (x, y) that make the equation true — not just "some" or "selected" points
2. Verify whether a given point lies on the graph of an equation by substituting its coordinates and checking whether both sides are equal
3. Graph equations in two variables by generating a table of values, plotting the points, and connecting them with a smooth curve or line
4. Distinguish between the graph of an equation in one variable (a point or set of points on a number line) and the graph of an equation in two variables (a curve in the coordinate plane)
5. Recognize that the graph of an equation in two variables can take many shapes — line, parabola, circle, exponential curve, and others — all of which are complete visual representations of the equation's solution set