Mr Northeast and Mr Southwest line in Coordinate County and

Mr. Northeast and Mr. Southwest line in Coordinate County and are good friends. Mr. Northeast lives at 20 East 28 North or (20,28), while Mr. Southwest lives at 10 West 14 South or (-10,-14). If the Streets are laid out in 1 mile square, Find the distance between the two men. Find the slope of the line that connects them. ---- The answer to this was M=7/5

I am now trying to answer this question:

Find the equation of the line from Mr. North\'s house and Mr. South\'s. Put it in the general form of an equation, i.e., Ax+By=C

Could you show me how you got this? Thank you in advance!

Solution

mr northeast = (20,28)

mr southwest = ( -10,-14)

slope = y2-y1 / x2 - x1

slope = -14 - 28 / -10 - 20 = 7/5

to find the equation take any one point and plug in the equation y = mx+ b

28 = 7/5 ( 20) + b

28 = 28 + b

solving for b we get

b = 0

hence equation is

y = 7/5 x

writing equation in Ax + B y = C FORM

5y = 7x

or 7x- 5y = 0