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Graphing Linear Equations

Graphing Linear Equations is a mapping process to diagram straight lines as objects. Mathematicians often diagram using Cartesian coordinate systems.

A Cartesian Coordinate System provides a central point of reference for an object and between objects. Cartesian coordinate systems are drawn by a horizontal “x” line bisecting a “y’ line forming a 90 degree right angle. Coordinates “x” and “y” are on a single plane, a flat surface.

The slope of a straight line is a measure of steepness. Slope is described by a change in Rise, divided by a change in Run.

Suppose coordinates (8, 7) and (4, 4), the slope, Δy / Δx, is:

(y2 - y1) / (x2 - x1) =

(7 - 4) / (8 - 4) =


Δy / Δx line slope

Graph of line showing linear slope as Δy / Δx.

How to Graph Linear Equations

By plugging values of “x” into a Linear Equation gives values of “y”.

Several coordinate solutions for y = 3x + 2:

x and y cartesian coordinate solution set.

“Y” values for “x” integer values -3 thru 3.

Choose two x and y coordinate solutions. Use them as points through which to plot the line.

Graph of coordinates for linear equation.

Graph of straight line equation y = 3x + 2 using coordinates (1, 5) and (-2, -4).



Many run and rise together look like steps.





Rise is a distance Δy as y2 - y1, and Run is a distance Δx as x2 - x1 (Reference diagram at right).

Slope = Rise / Run

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