SOLUTION: HI! Can you please assist me with this problem. Thank you A line has a slope of 8 and includes the points (10,9) and (a,1). What is the value of a? a=

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: HI! Can you please assist me with this problem. Thank you A line has a slope of 8 and includes the points (10,9) and (a,1). What is the value of a? a=      Log On


   

Question 1089997:
HI! Can you please assist me with this problem. Thank you

A line has a slope of 8 and includes the points (10,9) and (a,1). What is the value of a?
a=
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

The points (10,9) and (a,1) can be thought of as (x1,y1) and (x2,y2) respectively.

So,
(x1,y1) = (10,9)
(x2,y2) = (a,1)
which means
x1 = 10, y1 = 9
x2 = a, y2 = 1

The given slope is m = 8. Plug this m value and the x,y values discussed above, into the slope formula. Then solve for 'a'

m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

8+=+%281-9%29%2F%28a-10%29

8+=+-8%2F%28a-10%29

8%28a-10%29+=+%28-8%2F%28a-10%29%29%2A%28a-10%29 Multiply both sides by (a-10)

8%28a-10%29+=+-8

8a-80+=+-8 Distribute

8a-80%2B80+=+-8%2B80 Add 80 to both sides

8a+=+72

8a%2F8+=+72%2F8 Divide both sides by 8 to isolate 'a'

a+=+9

Answer: a = 9