Question

A path for a new city park will connect the park enterance and Maine Street, as shown below. The path should be perpendicular to Maine Street. What is the equation that represents the path?
y=________________

Answer 1

this is for the problem stated above ^^^

Answer 2

@SolomonZelman please help me

Answer 3

@Michele_Laino

Answer 4

please note that the line "Main Street" passes at point (3,3) and (1,-1)
so what is its slope?

Answer 5

hint: you have to apply this formula:
slope=\[=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]
where (x_1,y_1) and (y_1,y_2) are your points, namely (3,3) and (1,-1)

Answer 6

2/1?

Answer 7

oops...where (x_1,y_1) and (x_2,y_2) are the points (3,3) and (1-1)

Answer 8

ok! I call with m the slope of "Main Street", so m=2

Answer 9

Now "Park entrance" has to be perpendicular with respect to "Main Street". If I call with m' the slope of the line "Park entrance" then we have this equation:
\[m*m'=-1\]
so, please compute m' from my equation

Answer 10

It is very simple, because I set m=2 into my formula and I get:
\[2*m'=-1\]
please compute m'

Answer 11

ok so do you want me to substitute the new slope and sole for m?

Answer 12

ok! m'=...

Answer 13

if 2m'=-1, then \[m'=-\frac{ 1 }{ 2 }\]

Answer 14

3

Answer 15

Now, in order to find the equation of "Park entrance", please you have to apply this equation:
\[y-y _{1}=m'(x-x _{1})\]
where m'=-1/2 and (x_1,y_1)=(0,4), since "park entrance" passes at point (0,4) as you can see from your drawing.So we have:
\[y-4=-\frac{ 1 }{ 2 }x\]
please, simplify that equation and you will get your answer