How to Graph Linear Equations Without a Table

Drawing linear graphs is usually part of an algebra class.

A linear equation is a type of equation that makes a line when graphed. This set of equations take the form y = mx + b, where m is the slope and b is the y-intercept. When you solve linear equations by inputting a particular value for X, what you get out is a Y coordinate. The pairs of X and Y coordinates enable you to graph a linear equation without the use of a table.

Things You'll Need

• Graph paper
• Pencil
• Ruler

Instructions

1. Solve the equation for the first value. For example, if you want to plot Y = 5x + 2 at x={1,2,3...10} then solve for x=1:
   Y = 5(1) + 2 = 7
   This gives you the X,Y coordinates (1,7).

2. Plot the value from Step 1 on your graph. For example, to plot the coordinate (1,7), place your finger on the "X" axis of your graph at 7, then move your finger up 1 space (or however many squares on your graph paper represent a vertical unit of one). Place a dot at that point, then write "(1,7)" below the dot.

3. Solve the equation for the last value. In the example given, the last value is 10, so:
   Y = 5(10) + 2 = 52
   This gives you the X,Y coordinates (10,52).

4. Plot the values from Step 3 on your graph.

5. Join the two coordinates together with a ruler by drawing a line between the dots at (1,7) and (10,52) with a ruler. This is the graph of your linear equation.

Tips & Warnings

• The equation is a straight line, so you only need two points to draw the line for the equation. However, you may want to calculate three points to double-check your calculations.

References

• Math.com: Graphing Linear Equations