SOLUTION: A general equation of the family of lines perpendicular to 2x-5y=7 is...
THE ANSWER IS: 5x+2y=k (BUT HOW DO U GET THIS?) please tell me how and why this is the answer
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Question 38647: A general equation of the family of lines perpendicular to 2x-5y=7 is...
THE ANSWER IS: 5x+2y=k (BUT HOW DO U GET THIS?) please tell me how and why this is the answer
YOUR HELP IS MOST APPRECIATED, THANK YOU SO MUCH
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Start by putting the given equation in the slope-intercept form:
--> You can see that the slope, m, of the given line is
Now you want the family of lines that are perpendicular to this line, and as you know, perpendicular lines will have a slope that is the negative reciprocal of the given line...so the slope of the perpendicular lines will be the negative reciprocal of or
Since you are looking for the family of lines, you don't really care where these lines intercept the y-axis, so the y-intercept, b, can be any real number.
So now we have, in the slope-intercept form, the equation for the family of lines perpendicular to the given line:
Where b, the y-intercept is any real number. Now if you rearrange this equation:
Multiply both sides by 2 to clear the fraction.
Add 5x to both sides.
But since b is any real number, so 2b is any real number so you can let 2b = k, so finally you have:
.
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