Geometry hw, im suffering please help me. If you could also explain that'd be great. :)

Step-by-step explanation:

when a line is perpendicular to a given line, it uses the opposite reciprocal of the slope (basically flip the top and bottom numbers of the slope fraction and then change its sign from negative to positive or vice versa)

the slope of the given line is 1/4

the opposite would be -1/4

the reciprocal would be -4/1 or just -4

so the slope of this new line is -4

what we know so far is

y = -4x + b

since it has to go through point P (9, -2)

we’ll substitute 9 for x and -2 for y to find b

-2 = -4(9) + b

-2 = -36 + b

34 = b

so the final equation is

y = 4x + 34