Graphing linear equations is key to helping you with making observations or insights about the equation. Before we look at graphing linear equations, let's review graphing basics.
The image above is a Cartesian graph. The x-axis goes left to right, and the x-intercept is wherever a straight line crosses over or intersects this horizontal axis. The y-axis goes up and down, and the y-intercept is wherever a straight line crosses over or intersects this vertical axis. Think of this as a rectangular coordinate system formed with evenly spaced perpendicular lines. Each ordered pair of coordinates (x,y) denotes a singular point on the graph.
The graph of a linear equation can be drawn by finding which x values and y values solve for the equation of the line, meaning those values balance the equation. For example, (2, 5) is a valid graph point for the equation , because substituting 2 for x and 5 for y in the equation gives 5 = 2(2)+1, or 5=5. (0, 0) is not a solution because 0≠0+1, or 0≠1, and therefore is not a point on the line. Once you have collected several points, you can graph your equation.
Find the x-coordinate of a point on the graph by counting the number of spaces along the x-axis in accordance with the first value. Then, find the y-coordinate by looking at the second number and counting that number of spaces up or down the y-axis. For example, the point (2,3) would be two spaces to the right and three spaces up.