Make a conjecture about y = ax+b

[Dick]

Actually I've been away from my studies for a long time due to some health issues and have been struggling to get myself back to where I was 6 months ago, I have finals coming up too which is worrying!

Is my last post correct?

No, it's not. x+(a^2)x=(1+a^2)x. Don't you see why? Follow tiny-tim's clue about 'distributive law'.

 

[5ymmetrica1]

No, it's not. x+(a^2)x=(1+a^2)x. Don't you see why? Follow tiny-tim's clue about 'distributive law'.

Thanks, yes I understand why now.

so x = -ab / (1+a²) ?

 

[tiny-tim]

so x = -ab / (1+a²) ?

yup!

so y = … ?

and the slope = … ? ​

 

[5ymmetrica1]

yup!

so y = … ?

and the slope = … ? ​

y = a(-ab/(1+a²)) + b

I think this works? But I'm still not sure how I get -a from this answer

 

[tiny-tim]

y = a(-ab/(1+a²)) + b

I think this works? But I'm still not sure how I get -a from this answer

you seem to be frightened by algebra

grit your teeth and expand a(-ab/(1+a²)) and you should see how -a pans out

 

[5ymmetrica1]

yeah I worked it out today, I think this problem just got the better of me this week lol.

Thanks for your help everyone!

 

[tiny-tim]

good!

but since you need the practice, now try it another way …

your professor told you to find the the slope (let's call it "k") by finding the distance as a function of x, and to differentiate wrt x

instead, try finding the distance as a function of k, and differentiating wrt k (which will give you k directly, and may be quicker)

ie for the slope y = kx, find the coordinates where it intersects y = ax + b (both as a function of k), and then minimise that

to practise your algebra, show us what you get

(and which method do you think is quicker?)​