Graph a two-variable equation

Learning Objectives Identify the components of a coordinate plane (x-axis, y-axis, origin). Plot ordered pairs (x, y) accurately on a coordinate plane. Define what a solution to a two-variable equation represents. Create a table of values by substituting different values for one variable into a two-variable equation. Graph a two-variable linear equation by plotting multiple ordered pair solutions. Understand that the line drawn represents all possible solutions to the equation. Ever wonder how maps 🗺️ show exactly where things are? Or how a recipe 🧑‍🍳 tells you how much of each ingredient to use to get a perfect result? In this lesson, you'll learn how to draw pictures of equations with two variables. This helps us see patterns and relationships more clearly, making...

TermDefinitionExample Two-Variable EquationAn equation that contains two different unknown values, usually represented by letters like 'x' and 'y'.y = x + 3 or 2x + y = 7 Coordinate PlaneA flat surface formed by two intersecting perpendicular number lines, used to locate points.A graph paper grid with an x-axis and a y-axis. x-axisThe horizontal number line on a coordinate plane.When you plot the point (3, 2), the '3' tells you how far to move along the x-axis. y-axisThe vertical number line on a coordinate plane.When you plot the point (3, 2), the '2' tells you how far to move along the y-axis. OriginThe point where the x-axis and y-axis intersect on a coordinate plane. Its coordinates are (0, 0).The exact center of your graph paper where the two m...

The Coordinate Plotting Rule To plot an ordered pair $(x, y)$, start at the origin $(0,0)$. Move horizontally along the x-axis by 'x' units (right for positive, left for negative). Then, move vertically along the y-axis by 'y' units (up for positive, down for negative). This rule tells you exactly how to place any point on your graph paper. Always remember to move horizontally first, then vertically. The Solution Generation Rule To find solutions for a two-variable equation, choose a value for one variable (e.g., x), substitute it into the equation, and then solve for the other variable (e.g., y). This creates an ordered pair $(x, y)$ that is a solution. This rule helps you find specific points that lie on the line of your equation. You can pick any numbe...