Question 251373: 6. Find the equation of the line passing through (-1, -3) and perpendicular to y = -2x + 3.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
In point of fact, you cannot do what you ask to be done. You cannot find "the" equation of any line. That is because there are an infinite number of equations that represent any given line. What you can do is find "an" equation that fits the given parameters. Herewith the method:
Step 1: Solve the given equation for  in terms of everything else. In other words, put the given equation into slope-intercept form,  . In your problem, this is already done for you. Lucky you.
Step 2: Use the fact that perpendicular lines have slopes that are negative reciprocals, which is to say:
to determine the slope of the desired line by inspection of the coefficient on  in the slope-intercept form equation that resulted from the completion of step 1 and taking the negative reciprocal to derive the slope of the required line.
Step 3: Use the point-slope form, the coordinates of the given point, and the slope determined in Step 2 to write an equation of the desired line.
 )
where ) are the coordinates of the given point and  is the slope.
Step 4: If necessary, either because the problem instructions require it, or because you need to have the equation in a particular form in order to use it in a subsequent calculation, rearrange the equation into an appropriate form. Two very common form requirements are slope-intercept form (shown in step 1 of this procedure) and Standard Form,  . Note: Some texts require that A, B, and C be integers for proper standard form.
John
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