Though a line has a single graphed representation, it can have many different mathematical ones. A linear equation is the algebraic representation of a line. Different forms of linear equations are specific for different needed mathematical operations. The standard form of a linear equation, Ax + By = C, in which A, B and C are the coefficients and x and y are the variables, is better suited for calculations. The slope-intercept form, y = mx + b, in which the slope m gauges the line's incline or decline and b marks the point where the line intercepts the y-axis, helps to simplify graphing. You can change the standard form of a linear equation to its slope-intercept form through some simple mathematical manipulations.
Instructions
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1
Find a linear equation in standard form for example purposes, such as 6x + 2y = 10.
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2
Move the x-variable and its coefficient to the equation's right side by subtracting its amount from each side. For this example, subtracting 6x from both sides results in 6x + 2y - 6x = 10 - 6x, which becomes 2y = -6x + 10.
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Divide each of the equation's terms by the coefficient of the y-variable to convert to slope-intercept form. Finishing this example, dividing all terms by the coefficient of 2 results in 2y/2 = -6x/2 + 10/2, which becomes y = -3x + 5.