Definitions:

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 (x₁, y₁), 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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Converting to slope-intercept form

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Point-Slope and Standard Form

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Linear Equations in Slope Intercept Form

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X and Y Intercepts

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Slope Example

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Graphical Slope of a Line

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Slope of a Line 2

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Slope of a Line

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Linear equation from slope and a point

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Constructing the equation of a line given two points

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Multiple examples of constructing linear equations in slope-intercept form

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Length: 14:58