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**From Wolfram MathWorld:**

A linear equation is an algebraic equation of the form $$y = mx + b$$ involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Linear Equation -- from Wolfram MathWorld

$$m = \frac{rise}{run}$$ Change in y coordinates to change in x coordinates $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ **Standard Form:** [used when you know, or can find, the slope, m, and the y-intercept, b.] $$Ax + By = C$$ **Slope Intercept Form:** [used when you know, or can find, the slope, m, and the y-intercept, b.] $$y = mx + b$$ **Point Slope Form:** [used when you know, or can find, a point on the line (x_{1}, y_{1}), and the slope, m.] $$y - y_1 = m(x - x_1)$$

A general example to help you recognize patterns and spot the information you're looking for

Slope of the line: $$m = \frac{(-5)}{3}$$ Standard Form: $$5x + 3y = 2$$ Slope Intercept Form: $$m = \frac{(-5)}{3},\space intercept \space (0, \frac{2}{3})$$ $$y = \frac{(-5)}{3}x + \frac{2}{3}$$ Point Slope Form: $$y + 1 = \frac{(-5)}{3} (x + 1)$$

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