Answer:
[tex]y=-\frac{9}{7}x-2[/tex]
Step-by-step explanation:
Here, we have to convert the equation to slope-intercept form so we can find the perpendicular slope:
[tex]7x-9y=-5[/tex]
[tex]-9y=-5-7x[/tex]
[tex]y=-\frac{5}{9}+\frac{7}{9}x[/tex]
[tex]y=\frac{7}{9}x-\frac{5}{9}[/tex]
Since our slope is [tex]m=\frac{7}{9}[/tex], then that means the slope perpendicular to it is [tex]m=-\frac{9}{7}[/tex].
Now we find our new y-intercept so that the line will pass through the point (-7,7):
[tex]y=mx+b[/tex]
[tex]y=-\frac{9}{7}+b[/tex]
[tex]7=-\frac{9}{7}(-7)+b[/tex]
[tex]7=9+b[/tex]
[tex]-2=b[/tex]
Therefore, the equation of the new line is [tex]y=-\frac{9}{7}x-2[/tex]
