<PRE><B>Question 332068</B>
the line parallel to 2x-6y=-1 and containing the x intercept of 4x-3y=12. 
:
parallel lines have the same slope, find the slope of 2x - 6y = -1
-6y = -2x - 1
y has to be positive, multiply by -1
6y = 2x + 1
Divide by 6
y = {{{2/6}}}x + {{{1/6}}}
y = {{{1/3}}}x + {{{1/6}}}
the slope = {{{1/3}}}
:
Find the x intercept of 4x-3y=12.
x intercept occurs when y = 0, 
4x - 3(0) = 12
4x = 12
x = 3 is the x intercept
:
using the slope/intercept form; y = mx + b to find the equation
find b when y=0 and m=1/3 and x=3
0 = {{{1/3}}}(3) + b
0 = 1 + b
-1 = b
:
The desired equation: y = {{{1/3}}}x - 1 
;
:
Looks like this
{{{ graph( 300, 200, -6, 5, -6, 6, .33x-1, 1.33x-4, .33x+1.83) }}}
the desired equation is red</PRE>