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Graphing Linear Equations

Thanks to René Descartes, the French philosopher and mathematician, who supposedly was lying in bed and staring up at a fly on his ceiling, we have a fabulous way to graph equations. We now have what is known as the Cartesian Plane! We can use an ordered pair of coordinates to specify a point to indicate a specific orientation or location in space.

Lesson 1: Linear Equation Vocabulary

Before you can do anything, you need to know the basics. Understanding the basics is key as this will be your foundation.

Number Line: A number line has arrows at both ends which means it goes on indefinitely.


x-axis and y-axis: two number lines, one goes horizontally (x-axis) and the other vertically (y-axis).

The x- and y-axes give you dimensionality, so points can be plotted in a plane.

When plotting points, you move across the x-axis first then, you move up or down along the y-axis.

Think: x comes before y in the alphabet to help you remember this.

The 2-axis grid is called the Cartesian Plane or Cartesian Grid and is named after René Descartes.


coordinate pair (or ordered pair): how to describe a point's location on the Cartesian grid by the point of intersection on the x-axis and y-axis; (x, y)

abscissa: the value of the x in the ordered pair (x, y)

ordinate: the value of the y in the ordered pair (x, y)

Point A is located at (4, 4)
Point B is located at (–3, –5)

function: a table of ordered pairs that shows the relation between the domain (x values) and the range (y values) and how they correspond to one another.




Hint: An easy way to help you with the ordered pairs is to put parenthesis around the numbers in the columns. Check it out…
Now, the function table has given the ordered pairs that can be graphed!
(0, 4), (1, 5), and (-2, 2)

graphing the function: plotting the points of the function on a Cartesian plane/grid

All the points on the 'graph' are the solutions to the equation. This is the awesome part of graphing linear functions.

Look at a spot where the blue line crosses the intersection of two axes…(-5, -1) is one such place. Now, if you go back to the equation and use the Substitution Property, replacing the x with -5, guess what! y is -1! Isn't that the coolest thing?
Lesson 2: Finding the Slope

Now that you understand the vocabulary and have the foundation for linear equations you can move on to finding the slope and y-intercept!

slope yintercept

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