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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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Standard Form of a Line

The graph of the equation x = 4 is a vertical line. Because slope is undefined for vertical lines, the equation of this line cannot be written in slope-intercept form or point-slope form. Only nonvertical lines can be written in those forms. However, a vertical line can be written in standard form. For example,

x = 4

can be written as

1 Â· x + 0 Â· y = 4.

Every line has an equation in standard form.

Example

Finding the equation of a line

Write an equation in standard form with integral coefficients for the line l through (2, 5) that is perpendicular to the line 2x + 3y = 1.

Solution

First solve the equation 2x + 3y = 1 for y to find its slope:

 2x + 3y = 1 3y = -2x + 1 y The slope is The slope of line l is the opposite of the reciprocal of . So line l has slope and goes through (2, 5). Now use the point-slope form to write the equation:

 y - 5 Point-slope form y - 5 Distributive property y  = 2 3x - 2y = -4 Multiply each side by -2.

So 3x - 2y = -4 is the standard form of the equation of the line through (2, 5) that is perpendicular to 2x + 3y = 1.