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I have looked at previous post that were on similar topics in hopes of not having to create a new post but I seem to be stuck still.

Find an equation of the Plane that contains the line y=-2x+3 in the plane z=5, and goes through the point (2,-7,23)

General equation of plane:

f(x,y,z)=mx+ny+c

First I set up the equation of a plane using slopes from the equation of the line and values for the point it should pass through

23=-2(2)+n(-7)+3

then solved for y-slope

24=-7n

n=24/7

this gives me the function:

z=-2x-(24y/7)+3

I'm not sure my procedure was correct at all and I can't seem to figure out how to check this. If i plug in the values , I get the right z point, but this only tells me that I did my algebra correct (I hope :-!). I know I'm probably missing a major concept probably but some I cannot seem to make any progress on this problem.

Thanks for the help

## Homework Statement

Find an equation of the Plane that contains the line y=-2x+3 in the plane z=5, and goes through the point (2,-7,23)

## Homework Equations

General equation of plane:

f(x,y,z)=mx+ny+c

## The Attempt at a Solution

First I set up the equation of a plane using slopes from the equation of the line and values for the point it should pass through

23=-2(2)+n(-7)+3

then solved for y-slope

24=-7n

n=24/7

this gives me the function:

z=-2x-(24y/7)+3

I'm not sure my procedure was correct at all and I can't seem to figure out how to check this. If i plug in the values , I get the right z point, but this only tells me that I did my algebra correct (I hope :-!). I know I'm probably missing a major concept probably but some I cannot seem to make any progress on this problem.

Thanks for the help

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