Consider the standart form of equation:

\(Ax+By=C\)

Isolate the variable y term on one side of the equation:

\(By=-Ax+c\)

Divide both sides of the equation with B to write the equation in slope intercept form:

\(\displaystyle{y}=-\frac{{A}}{{B}}{x}+\frac{{C}}{{B}}\)

This implies that the slope of an equation written in standart form is \(\displaystyle-\frac{{A}}{{B}}\), therefore the slope of \(5x+2y=10\) is \(\displaystyle-\frac{{5}}{{2}}\)