SOLUTION: Two lines L1: 2y-3x-6=0 ad l2: 3y+x-20=0 intersect at a point A. Another line L4 is parallel to L1 and passes through (-1,3) find the x and y- intercepts L4

Algebra ->  Finance -> SOLUTION: Two lines L1: 2y-3x-6=0 ad l2: 3y+x-20=0 intersect at a point A. Another line L4 is parallel to L1 and passes through (-1,3) find the x and y- intercepts L4       Log On


   

Question 1189034: Two lines L1: 2y-3x-6=0 ad l2: 3y+x-20=0 intersect at a point A. Another line L4 is parallel to L1 and passes through (-1,3) find the x and y- intercepts L4
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
two equations are:

2y - 3x - 6 = 0 = L1
3y + x + 20 = 0 = L2

third equation is the line parallel to 2y - 3x - 6 = 0 and passing through the point (-1,3).

if parallel, it has the same slope as L1.

the slope intercept form of L1 is calculated below:

start with 2y - 3x - 6 = 0
add 6 to both sides to get 2y - 3x = 6
add 3x to both sides to get 2y = 3x + 6
divide both sides by 2 to get y = 3/2 * x + 3

that's the slope intercept form of L1.
L4 will have the same slope, so L4 equation will be:
y = 3/2 * x + b
b is the y-intercept.
since L4 passes through the point (-1,3), then replace y with 3 and x with -1 to get:
3 = 3/2 * -1 + b
simplify to get:
3 = -3/2 + b
add 3/2 to both sides to get:
3 + 3/2 = b
combine like terms to get:
9/2 = b

the equation of L4 parallel to L1 is y = 3/2 * x Z+ 9/2

the graph of L1 and L4 is shown below.



the blue line is L4.
you can see that the line passes through the point (-1,3).
can also see that the vertical separation between the red line and the blue line is always 1.5 units.