# Write the equation of the line parallel to 4x+3y=9 and passing through the point (-6,2) Write an equation for the line parallel to the line `4x+3y=9` and passing through the point (-6,2)

Parallel lines have the same slope. Writing the given line in slope-intercept form we have:

`4x+3y=9`

`3y=-4x+9`

`y=-4/3x+3` so the slope is `-4/3`

** If a line is in general form `Ax+By=C` then...

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Write an equation for the line parallel to the line `4x+3y=9` and passing through the point (-6,2)

Parallel lines have the same slope. Writing the given line in slope-intercept form we have:

`4x+3y=9`

`3y=-4x+9`

`y=-4/3x+3` so the slope is `-4/3`

** If a line is in general form `Ax+By=C` then the slope is `m=-A/B`

The required line has slope `-4/3` and contains the point (-6,2).

We can use the point-slope form of the line: given `m` and a point `(x_1,y_1)` the equation of the line is `y-y_1=m(x-x_1)`

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The equation of the required line is `y-2=-4/3(x+6)`

In slope-intercept form the equation is `y=-4/3x-6`

In general form `4x+3y=-18`

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