Question 430313
How do you determine the value of r so the line passes through each pair of points has the given slope? 
Example. 
(10,r),(3,4), m = -2/7 

METHOD 1: Use the given slope and point to find the equation in standard form:

y - yo = m(x -xo)
y - 4 = (-2/7)(x - 3)
y -4 = (-2/7)x + 6/7
y = (-2/7)x + 6/7 + 4
y = (-2/7)x + 6/7 + 28/7
y = (-2/7)x + 34/7

(10,r) is the solution of above equation,we substitute it into the equation and find r:

r = (-2/7)(10) + 34/7 = -20/7 + 34/7 = 14/7 = 2

so r = 2

METHOD 2: USE Slope and two points

By slope formula:

m = (y2 -y1)/(x2-x1)

(10,r),(3,4), m = -2/7 

(r-4)/(10 -3) = -2/7
r-4 = (-2/7)(7)
r -4 = -2
r = -2 + 4
r = 2

There you go! you can use any method to find r:)
John10