given an equation, find an equation of a line.. too many letters and confused

jacknowlin

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Sep 24, 2018
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2
Hi,

The question asks:

Given ax+by = 1, find the equation of the line which has twice the x-intercept and twice the slope. Write your answer in the form of Px+Qy = 1.

I first changed the first equation to 2ax + by = 1 because of the "twice the x intercept"

Then i put the equation into slope intercept: by=-2ax +1

then doubled the slope: by = -4ax +1

Then wrote the answer in the asked form: 4Px+Qy = 1

I feel like I definitely did this problem wrong because it doesn't really make any sense to me since the first equation is a given, so I feel like doubling the slope to 2ax+by≠1 and the problem wouldn't work.

How else should I approach this problem?
 
Hi,

The question asks:

Given ax+by = 1, find the equation of the line which has twice the x-intercept and twice the slope. Write your answer in the form of Px+Qy = 1.

I first changed the first equation to 2ax + by = 1 because of the "twice the x intercept"

Then i put the equation into slope intercept: by=-2ax +1

then doubled the slope: by = -4ax +1

Then wrote the answer in the asked form: 4Px+Qy = 1

I feel like I definitely did this problem wrong because it doesn't really make any sense to me since the first equation is a given, so I feel like doubling the slope to 2ax+by≠1 and the problem wouldn't work.

How else should I approach this problem?

You appear to have assumed that a is the x-intercept. It isn't.

And in your answer, you should be expressing "P" and "Q" in terms of a and b; P and Q are not known values that you can use.

A straightforward method of solution would be to solve ax+by=1 for y, so you can see the actual slope, and set y to 0 so you can find the actual x-intercept. Then you can use the new slope and x-intercept, in the point-slope form, to write an equation for the new line, and then put that in the desired form.

Please show how far you can get this way.
 
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