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Linear Equations

A linear equation in two variables, often written as \( y = mx + b \), describes a line in the \( xy \)-plane. The line consists of all the solution pairs \( (x_0, y_0) \) that make the equation true.

For example, in the equation, \( y = 2x -1 \), the line would pass through the points \( (0,-1) \) and \( (2, 3) \) because these ordered pairs are solutions to the equation.

The coefficient \( m \) is the slope of the graph, and the constant \( b \) is the \( y \)-intercept.

The slope of a graph is the ratio between the rate of change of \( y \) and the rate of change of \( x \), so for two points on a graph \( p_1=(x_1,y_1) \) and \( p_2=(x_2,y_2) \), slope between them is:

\[ m = \frac{y_2 - y_1}{x_2-x_1}\]

Note by Arron Kau
2 years, 11 months ago

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