Kristen loves shortcuts. She figured out that she can find $x$- and $y$-intercepts for any line without graphing! For example, she knows that the $x$-intercept for $5x-3y=15$ is $\left(3,0\right)$ just by examining the rule.  

1. What is her shortcut?

   Hint (a):

   She knew the $x$-intercept occurred when $y=0$.

2. Does this shortcut work for the $y$-intercept? Try it and then test your result by changing $5x-3y=15$ into $y = mx + b$ form.

   Step 1(b):

   $5\left(0\right)-3y=15$

   Step 2(b):

   $y=-\frac{5}{3}x-5$

3. Use this shortcut to find the $x$- and $y$-intercepts of $3x-2y=24$.

   Step (c):

   $3x-2\left(0\right)=243\left(0\right)-2y=24$