Find the values of a and b in the given straight line equation

AI Thread Summary
The discussion focuses on finding the values of a and b in a straight line equation. The initial approach involves determining coordinates based on x and y intercepts, leading to the equation -3 = (b-0)/(0-a), resulting in b = 3a. Further calculations yield a = 2√10 and b = 6√10. Participants confirm the correctness of these values and express similar methods in their approaches. The conversation concludes with a friendly exchange, maintaining a collaborative tone.
chwala
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Homework Statement
see attached
Relevant Equations
straight lines
Find the problem below;
1640819951710.png


My approach,
if##x=0##, then ##y=b## and if ##y=0##, then ##x=a##, therefore our co-ordinates are ##(a,0)## and ##(0,b)##. The gradient will give us,
$$-3=\frac {b-0}{0-a}$$
It follows that, ##b=3a##, therefore
$$20=\sqrt {(3a-0)^2+(0-a)^2}$$
$$400=9a^2+a^2$$
##a=2\sqrt 10## and ##b=6\sqrt 10##

Any other approach on this.
 
Last edited:
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chwala said:
##a=2\sqrt 10## and ##y=6\sqrt 10##

Any other approach on this?

I'm pretty sure you mean the ##b=6\sqrt{10}## .

My approach was about the same as yours.
 
Last edited:
SammyS said:
I'm pretty sure you mean the ##b=6\sqrt{10}## .

My approach was about the same as yours.
Sammy happy new year 2022 Mate!Let me amend it, sure.
 
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