Answer:
y = (9/2)x + 26.5
Explanation:
Lets rewrote the equation in standard format of y = mx + b, where m is the slope and b is the y-intercept.
-2x-9y = 1
-9y = 2x + 1
y = -(2/9)x - (1/9)
The slope of this line is -(2/9)
A line that is perpendicular to this line will have a slope that is the negative inverse of -(2/9). That would be (9/2). So a perpendicular line will have the form of y = (9/2)x + b. Any value of b can be chosen and the lines will still be perpendicular to each other. However, we want to find a value of b that will force the line through point (-7,-5). This is done by using the point in the above equation and solving for b:
y = (9/2)x + b
-5 = (9/2)(-7) + b for point (-7,-5)
-5 = -(63/2) + b
b = -5 + (63/2)
b = -5 + 31.5
b = 26.5
The equation is y = (9/2)x + 26.5
See the attached graph.