Consider the line represented by the equation 5x+2y=10. How is the slope of the line...

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 ${\displaystyle -\frac{5}{2}}$