Can someone please check my work?
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
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
@Reiny Could you please show me how to fix the problem?
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.
To check your work, we can use the point-slope form of the equation to see if both points satisfy the equation:
Point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Let's use the first point (1, 20):
y - 20 = (-31/14)(x - 1)
y - 20 = (-31/14)(x) + (31/14)(1)
y - 20 = (-31/14)x + 31/14
Now let's use the second point (8, 4.5):
y - 4.5 = (-31/14)(x - 8)
y - 4.5 = (-31/14)(x) + (31/14)(8)
y - 4.5 = (-31/14)x + 31/2
Both equations are consistent with the points (1, 20) and (8, 4.5), so it seems like your answer is correct. Good job!