SOLUTION: The lines y=4x-10 and y=x-1 intersect at the point T. Find the equation of the line with gradient -2/3 that passes through the point T.

Algebra ->  Finance -> SOLUTION: The lines y=4x-10 and y=x-1 intersect at the point T. Find the equation of the line with gradient -2/3 that passes through the point T.       Log On


   

Question 1185850: The lines y=4x-10 and y=x-1 intersect at the point T. Find the equation of the line with gradient -2/3 that passes through the point T.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The lines y=4x-10+and y=x-1+intersect at the point T.
y=4x-10+....eq.1
y=x-1+..........eq.2
----------------------------if left sides equal, right sides are equal to
4x-10+=x-1.....solve for x
4x-x+=10-1
3x+=9
x+=3
find y
y=3-1+..........eq.2
y=2+
=> the point T is at (3,2)

then, the equation of the line with gradient -2%2F3 that passes through the point T is:
y-y%5B1%5D=m%28x-x%5B1%5D%29
y-2=-%282%2F3%29%28x-3%29
y-2=-%282%2F3%29x%2B%282%2F3%293
y-2=-%282%2F3%29x%2B2
y=-%282%2F3%29x%2B2%2B2
y=-%282%2F3%29x%2B4