Question

A rectangle is graphed on the coordinate grid.

Answer 1

Side s

(4,1)(1,4)
slope = (4-1)/(1-4) = 3/-3 = -1

y =  mx + b
1 = -1(4) + b
b = 5

equation of side s:
y = -x + 5

Answer 2

With two points you can define a line.

So, the line parallel to s is q, which has these two points: (3,6) and (6,3)

There are different ways to get the line. For instance, this one:

y = a*x+b,

a = slope = difference_y/difference_x = (3-6)/(6-3) = -1,

y = -x + b,

Now use any point, say (3,6) to get b:

6 = -3+b-> b = 9,

line is y = -x + 9,

It checks out in the other point: (6,3) --> 3 = -6+9 = 3. Good.

Other method could be:

y-y2 = a*(x-x2), where (x2,y2) is one of the two points and a is the slope as defined before.

Hope it helps!