Question 1189034
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.


<img src = "http://theo.x10hosting.com/2021/122101.jpg" >


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.