Lines intersect when their $y$-coordinate and $x$-coordinate are equal.

We know $y= -x+a$ and $y=bx$, so we set the right hand sides equal to each other to receive the $x$-coordinate for the intersection.

$\displaystyle -x+a = bx$

$\displaystyle a = bx+x$

$\displaystyle a = x(b+1)$

$\displaystyle x = \frac{a}{b+1}$

This is the value of $x$ at the intersection, so we may put this value into the equations for $y$ to find the $y$-coordinate at the intersection.

$\displaystyle y= bx$

$\displaystyle y=b \left( \frac{a}{b+1} \right)$

$\displaystyle y=\frac{ab}{b+1}$

Putting $x= \frac{a}{b+1}$ into $y=-x+a$ also yields $y=\frac{ab}{b+1}$, but I'll leave it to you to work out.