The inclination of Palm Street on the map is given by the slope of the line joining the given points:
(5-1)/(11-(-1))=4/12=⅓, so Pepperdine Street has a slope = -(1/⅓)=-3 because it's perpendicular. Therefore: (y-7)/(7-4)=-3, (y-7)/3=-3, y-7=-9, y=-2. Pepperdine St passes through (7,-2).
The equation of the line corresponding to Pepperdine St is:
y-7=-3(x-4) (slope-point form),
y=-3x+12+7=-3x+19. Note that (7,-2) is on this line.