Answer:
[tex]\[y=-\frac{4}{9}x+11\][/tex]
Step-by-step explanation:
Equation of the given line is [tex]\[-9x+4y=8\][/tex]
Slope of the line = [tex]\[\frac{9}{4}\][/tex]
Slope of the perpendicular line = [tex]\[-\frac{4}{9}\][/tex]
Equation of the line perpendicular to the given line is [tex]\[y=mx+c\][/tex]
[tex]\[y=-\frac{4}{9}x+c\][/tex]
But this line passes through (9,7)
Substituting the values in the equation:
[tex]\[7=-4+c\][/tex]
=> [tex]\[c=7+4=11\][/tex]
So the overall equation of the parallel line is given by [tex]\[y=-\frac{4}{9}x+11\][/tex]
