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

[chwala]

Homework Statement

see attached

Relevant Equations

straight lines

Find the problem below;

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.

 

[SammyS]

$a=2\sqrt 10$ 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.

 

[chwala]

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.