ANSWER
[tex] - \frac{5}{3} [/tex]
EXPLANATION
The given line has equation
[tex]3y + 5x = 4[/tex]
Rewrite the equation in the form:
[tex]y = mx + b[/tex]
Add -5x to both sides.
[tex]3y + 5x - 5x = - 5x + 4[/tex]
[tex]3y = - 5x + 4[/tex]
Divide through by 3.
[tex]y = - \frac{5}{3}x + \frac{4}{3} [/tex]
Comparing to the slope intercept formula,
[tex]m = - \frac{5}{3} [/tex]
The slope is
[tex] - \frac{5}{3} [/tex]
