write the equation of a line parallel to line 4x-6y=1 that intersects the function 3x-2y=12 at its x-intercept

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Parallel lines have the same slope. The slope is the gradient which is m. in the form y=mx+b

5x-6y=1

-6y=-5x+1

6y=5x-1

y=5/6x-1/6

so slope =5/6.

The two lines meet at the x intercept of 3x-2y=12

2y=3x-12

y=3/2x-6 so coordinates at x=0 is y=-6

Gradient= change in y divided by change in x

so equation of our line (y+6)/(x-0)= 5/6

6y+36=5x-0

6y=5x-36

y=5/6x-6

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