SOLUTION: Write the equation of the line that contains the point ( - 1, 4) and is perpendicular to the line x - 2y = 6. Express final equation in standard form
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-> SOLUTION: Write the equation of the line that contains the point ( - 1, 4) and is perpendicular to the line x - 2y = 6. Express final equation in standard form
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Question 242329: Write the equation of the line that contains the point ( - 1, 4) and is perpendicular to the line x - 2y = 6. Express final equation in standard form Answer by solver91311(24713) (Show Source):
Technically, you cannot do what you ask. You cannot write "the" equation of a line. The set of equations that represent a given line has an infinite number of elements. You can, however, derive an equation which solution set is a set of ordered pairs that represent a straight line in .
First re-arrange the given equation so that it is in slope-intercept form, i.e. . Then determine the slope of the given line by inspection. Take the negative reciprocal of the slope of the given line as the slope of the desired line because:
Using the slope determined from the previous step and the coordinates of the given point, apply the point-slope form of an equation of a line:
Where is the derived slope and are the coordinates of the given point.
Rearrange the equation into standard form, namely:
Some texts require that A, B, and C be integers for proper standard form.
