# CHARACTERISTICS OF LINEAR GRAPH

**Topics:**Linear equation, Quadratic equation, Quintic equation

**Pages:**2 (219 words)

**Published:**December 3, 2014

CHARACTERISTICS OF LINEAR GRAPH

Definition: A linear equation in two variables is an equation which may be written in the form y = mx + b where m, and b are real numbers.

The graph of a linear equation is a non-vertical line with slope m and y-intercept b. Every non-vertical line is the graph of a linear equation of the form y = mx + b The x-intercept occurs when y = 0.

Therefore we find the x-intercept by solving mx + b = 0.

Subtract b from both sides and then divide both sides by m to obtain . The y-intercept occurs when x = 0.

Therefore the y-intercept is b.

To sketch the graph of a linear equation, plot any two points whose coordinates satisfy the equation and draw the line passing through the two points. Plotting the two intercepts is generally a good idea. Any time two independent pieces of information are known about a line L it is possible to determine the linear equation whose graph is that line L. The most important fact used in this process is: A point is on the graph of an equation if and only if its coordinates satisfy the equation. That is, a point (t, k) is on the graph of an equation f if and only if substituting t and k into the equation yields a true statement.

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