Explanation:
a.
remember, the slope is (y coordinate difference / x coordinate difference) when going from one point on the line to another point on the line.
let's just use the first 2 points (29, 97) and (18, 64).
x changes by -11 (29 to 18).
y changes by -33 (97 to 64)
the slope is -33/-11 = 3
b.
no it does not matter. a line represents all points that satisfy the same slope ratio.
other 2 points - let's use the last 2 points (14, 52) and (-27, -71).
x changes by -41 (14 to -27).
y changes by -123 (52 to -71).
the slope is -123/-41 = 3
yes identical as expected.
c.
the easiest way to write the equating of the line with slope and 1 point is the point/ slope form :
y - y1 = a(x - x1)
"a" is again the slope, (x1, y1) is the point on the line.
let's use point (18, 64).
y - 64 = 3(x - 18) = 3x - 54
y = 3x + 10
d.
no, it does not matter. because we are using the x AND y coordinates, which follows the same slope ratio as every other point on the line.
e.
by putting the x and y coordinates into the equation and see, if the equation remains true. if all given points keep the equation true, then our equation is correct.