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

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) (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.

RELATED QUESTIONS
Two lines L1: 2y-3x-6=0 ad l2: 3y+x-20=0 intersect at a point A. Find the coordinates of... (answered by Alan3354)

Two lines L1 :2y-3x-6=0and L2 :3y+x-20=0 intersect at point A. A third line L3 is... (answered by MathLover1,Alan3354)

Two lines L1: 2y-3x-6=0 ad l2: 3y+x-20=0 intersect at a point A. A third line L3 is... (answered by Theo)

Two lines L1 :2y-3x-6=0and L2 :3y+x-20=0 intersect at point A. A third line L3 is... (answered by Boreal)

L1 is the straight line 2x+3y+6=0. without finding the gradient of L1, find the equation... (answered by josgarithmetic)

can you help me answer this :) Given; L1: 2x+4y-8=0 and L2: 2x+3y-16=0 A. Find the... (answered by josgarithmetic)

For each pair of lines, determine if they are parallel, perpendicular or neither. A. (answered by Boreal)

A line L1 passes through point[1,2]and has a gradient of 5.Another line L2 is... (answered by mananth)

line L1 and L2 has equation (x-3)/2 = (y-4)/-1 = (z+1)/1 and (x-5)/4 = (y-1)/3 = (z-1)/2. (answered by Edwin McCravy)