How to Graph a Function

Step-by-Step Guide

1. 1

   Step 1: Recognize linear functions as simple

   There is one variable and one constant, written as F(x)ory=a+bx{\displaystyle F(x)ory=a+bx} in a linear function, with no exponents, radicals, etc.
   
   If you've got a simple equation like this, then graphing the function is easy.
   
   Other examples of linear functions include:
   F(n)=4−2n{\displaystyle F(n)=4-2n} y=3t−120{\displaystyle y=3t-120} F(x)=23x+3{\displaystyle F(x)={\frac {2}{3}}x+3}
2. 2

   Step 2: easily-graphed lines

   The y-intercept is where the function crosses the y-axis on your graph.
   
   In other words, it is the point where x=0{\displaystyle x=0}.
   
   So, to find it, you simply set x to zero, leaving the constant in the equation alone.
   
   For the earlier example, y=2x+5{\displaystyle y=2x+5}, your y-intercept is 5, or the point (0,5).
   
   On your graph, mark this spot with a dot. , In your example, y=2x+5{\displaystyle y=2x+5}, the slope is "2." That is because 2 is right before the variable in the equation, the "x." Slope is how steep a line is, or how high the line goes before going to the right or left.
   
   Bigger slopes mean steeper lines. , Slope is about steepness, and steepness is simply the difference between movement up and down and movement left and right.
   
   Slope is a fraction of rise over run.
   
   How much does the line "rise" (go up) before it "runs" (goes to the side)? For the example, the slope of "2" could be read as 2up1over{\displaystyle {\frac {2up}{1over}}}.
   
   If the slope is negative, that means the line goes down as you move to the right. , Once you know your slope, use it to plot out your linear function.
   
   Start at your y-intercept, here (0,5), and then move up 2, over
   1.
   
   Mark this point (1,7) as well.
   
   Find 1-2 more points to create an outline of your line. , To prevent mistakes or rough graphs, find and connect at least three separate points, though two will do in a pinch.
   
   This is the graph of your linear equation!
3. 3

   Step 3: like y=2x+5{\displaystyle y=2x+5}.

4. 4

   Step 4: Use the constant to mark your y-intercept.

5. 5

   Step 5: Find the slope of your line with the number right before the variable.

6. 6

   Step 6: Break the slope into a fraction.

7. 7

   Step 7: Starting at your y-intercept

8. 8

   Step 8: follow your "rise" and "run" to graph more points.

9. 9

   Step 9: Use a ruler to connect your dots and graph your linear function.

Detailed Guide

About the Author