Can someone please check my work?

Question

Question~
Find the point-slope form of the equation that goes through these two points. (1, 20) and (8, 4.5)

My Answer~
Y= y2-y1/x2-x1
(4.5-20)/(8-1)
=
-15.5/7
Rewrite -15.5/7 as (-15.5)/7
Rewrite -15.5 as -31/2
=
(-31/2)
(7/1)
Divide:
(-31/2) / (7/1)
=
-31/14
Y= -31/14x+b
(1,20) = x
20=-31/14+b
b=20+ 31/14
20*14/14=280/14
311/14=b
Y=-31/14x+311/14

Answer 1

wow.

slope = (4.5-20)/(8-1)
= -15.5/7 ----> top and bottom times 10
= -155/70 = -31/14

so y = (-31/14)x + b
sub in the point (1,20)
20 = -31/14 + b
b = 20 + 31/14 = 311/14

y = (31/14)x + 311/14

you are correct,

I object to the statement:
(1,20) = x, it is meaningless

Answer 2

@Reiny Could you please show me how to fix the problem?

Answer 3

There is really no problem with your solution, other than the fact it seems too complicated.
e.g. in the slope, compare your steps with mine

instead of saying:
(1,20) = x , say ...
for the given point (1,20), x = 1 and y = 20

notice you have the same equation as I have.