Distance in coordinate system

Question

The line $y = \frac{3}{4}x + m$, where $m\ne0$ , intersects the $x$-axis at point $P$ and the $y$-axis at $Q$.

Which is larger:

• Quantity 1 : The distance from $P$ to the origin $( 0 , 0)$
• Quantity 2 : The distance from $Q$ to the origin $( 0 , 0)$

I don't know how to approach this question

/ Daniel M

Answer 1

Hint: Any line given by $y=ax+b$ intersects the $x$-axis in $(-\frac{b}{a},0)$ and the $y$-axis in $(0,b)$.

Using that, you just need to compute distances of both points to the origin. Note that, since they have one coordinate equal to 0, the distance will be the absolute value of the non-zero one.

Answer 2

setting $y=0$ we get $$x=-\frac{4m}{3}$$in the other case we get $$y=m$$ the distances are $\frac{4}{3}|m|>|m|$