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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
3 years, 2 months ago