ANSWER
[tex]-\frac{5}{7}[/tex]EXPLANATION
We want to find the slope of the given line:
[tex]-5x-7y=-9[/tex]First, put the line in the slope-intercept form:
[tex]y=mx+b[/tex]where m = slope; b = y-intercept
Therefore, we have that:
[tex]\begin{gathered} -7y=5x-9 \\ \Rightarrow y=-\frac{5}{7}x+\frac{9}{7} \end{gathered}[/tex]From the equation above, we see that the slope of the line is:
[tex]-\frac{5}{7}[/tex]