SOLUTION: Given the points" A(2,6) B(-4,10) C(8,15) Answer the following: Equation of AB in slope intercept form?? How do you do this?

Algebra ->  Rational-functions -> SOLUTION: Given the points" A(2,6) B(-4,10) C(8,15) Answer the following: Equation of AB in slope intercept form?? How do you do this?      Log On


   

Question 21272: Given the points" A(2,6) B(-4,10) C(8,15)
Answer the following: Equation of AB in slope intercept form?? How do you do this?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
First you have to find the slope of line AB.
m=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+
m=%2810-6%29%2F%28-4-2%29=4%2F-6=-2%2F3

The equation of the line is in the form y=mx+b, where m is the slope that you just found, (x,y) represents any point on the line, either point A(2,6) or B(-4,10).

Use: m=-2%2F3, x=2, and y=6, and solve for b.
y=mx+b
6=%28-2%2F3%29%2A2+%2B+b

Multiply both sides by the denominator, which is 3
3%2A6=3%2A%28-2%2F3%29%2A2+%2B+3%2Ab
18+=+-4+%2B+3b
22=+3b
b+=+22%2F3

Final Answer:
y+=+mx+%2B+b
y=+%28-2%2F3%29x+%2B22%2F3+

Check: Substitute the values of B(-4,10), and see if it works:
y+=+%28-2%2F3%29x+%2B+22%2F3
10+=+8%2F3+%2B+22%2F3+
10+=30%2F3+
It checks!

What about point C(8,15)?? You asked for the equation of line AB, and it seems that point C is just another point. Perhaps it was to be used in a different problem.

NOTE: Math is not usually as hard as it sometimes looks! Don't let anyone blow you away by making it look harder than it really is. It should NOT be intimidating!!

R^2 at SCC