(11,5) and (-1,1) (4,7) and (7,y)

Question

A city designer is drawing the road map for a new housing development. Palm St. runs through the coordinates (11,5) and (-1,1) on the map. Pepperdine St. is going to run perpendicular to Palm St. The coordinates of Pepperdine St. are (4,7) and (7,y). What is the value of y? What is the equation for the line representing Pepperdine St. in slope-intercept form?

Answer 1

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.