We have the line $g$ that passes through $A(-3;-4)$ and $B(6;2)$. Find the coordinates of $M$ and $N$ where $g$ crosses the $x$-axis and $y$-axis.
When we make a graph, we see that $M(3;0)$ and $N(0;-2)$. Is there a general formula that I can use without making a reasonable graph to see the coordinates?
The equation of your line is $y=mx+n$. $m$ denotes the slope $$m=\frac{y_2-y_1}{x_2-x_1}=\frac{2}{3}$$ and we get $n=-2$. Now we can compute the intersection points with the axis: $$x=0,y=-2$$ and $$y=0,x=3$$