Graphing y = mx + b

The equation y = mx + b will always produce a graph of a perfectly straight line. The line may go upwards or downwards. It can even be horizontal or vertical!

There are two ways to graph a line when it's equation is written in slope-intercept form: y = mx + b.
1. Use a table of values
2. Use the intercept and the slope

Using a Table of Values

Creating a table of (x, y) coordinates to plot in order to create the image of the graph is the most common approach to graphing. You can pick as many x-values as you'd like, there is no limit. Each x-value gets substituted into the equation. The answer is always the y-coordinate. Together they create points (x, y) to plot on a coordinate axis to create your line.

Step One: create a table of values by choosing values for x.
Step Two: Substitute each value into the equation for x. Simplify to get the answer, the y-coordinate. Step 3: Then create ordered pairs using your x-values and y-values.
Step Four: Plot them on a coordinate axis and you are done! You can use the same steps for every equation.

Example 1: Graph y = 3x + 4

ex 1 ex 2 ex 3 ex 4

Example 2: graph y = 2x + 5.

ex 5 ex 6 ex 7 ex 8

Example 3: graph y = -3x + 7.

ex 1 ex 9 ex 10 ex 11

Example 4: graph y = -2x + 3.

ex 1 ex 12 ex 13 ex 14

Using the y-intercept and the Slope

The second method to graph a line is using the numbers they give you in the equation in order to graph the line.
It is harder at first, but it will save you time compared to making a table of values.

The 2 numbers in the equation are called the slope and the intercept. The intercept is plotted on the y-axis at its appropriate location.
The slope is drawn with your pencil at the point for the y-intercept. Then a second point is made.
Connect the 2 points making a line with a ruler. Put arrows at both ends of your line. This shows the graph goes on in both directions. And you are done! No calculations necessary to graph a line. And the best part is it works the same for all lines!

Let's look at an example:
Graph y = 4x - 6
The slope is always the number infront of the variable x. The slope is 4.
The y-intercept is the number not with the variable x. The y-intercept is -6.

Let's look at an example:
Graph y = 7x + 3
The slope is always the number infront of the variable x. The slope is 7.
The y-intercept is the number not with the variable x. The y-intercept is 3.

Let's look at an example:
Graph y = -3/4x + 7
The slope is always the number infront of the variable x. The slope is -3/4.
The y-intercept is the number not with the variable x. The y-intercept is 7.

Let's look at an example:
Graph y = 2/3x + 3
The slope is always the number infront of the variable x. The slope is 2/3.
The y-intercept is the number not with the variable x. The y-intercept is 3.

The difficult part to remember using this method is when adding the slope to the graph. I gave 4 different examples. Each one had slope. But 2 were fractions and 2 were whole numbers.

Rule: If the slope value is not a fraction, make it one by turning it into a fraction by giving it a denominator of 1. If the slope value is already a fraction skip this step.
1. The number on the top of the fraction is how many spaces to move up (if it's a positive number), and down (if it's a negative number).
2. The number on the bottom of the fraction is how many spaces you move right, then put a point at that location. Connecting this point to the y-intercept's point will create your graph.
3. Remember you can also choose not to use this technique and use a Table of Values to graph the line instead. It creates the same answer. It is your choice which technique you use.