Solve the equation for y; the slope will be the coefficient of the x-term:
3x - 5y = 10
-5y = -3x + 10 (subtract 3x from both sides)
y = (3/5)x - 2 (divide both sides by 5)
The slope is 3/5; the y-intercept occurs at -2.
$${\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{10}} \Rightarrow {\mathtt{x}} = -{\mathtt{5}}$$
Easy x=-5 y appears in a xyz coordinate equations like
$${\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{34}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\sqrt{{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{z}}}} \Rightarrow {\mathtt{y}} = {\frac{\left({\sqrt{{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{z}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{34}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{{\mathtt{3}}}}$$
.