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Plot Equation with 3 variables in 3 dimensions











































Plot the following equation in three dimensions. Determine the x-intercept, y-intercept, and z-intercept.

2x + 3y + 4z = 12

Is the result a line, a plane, or a solid geometric figure?


Comments for Plot Equation with 3 variables in 3 dimensions

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Jul 06, 2012
Plot Equation with 3 variables
by: Staff


The answer:

The resulting figure is a plane (a flat surface) which intersects all three axes.

The easiest way to draw the plane is to compute the x, y, and z intercepts first. Once you have all three intercepts, just connect the three points on a three dimensional coordinate system.

x-intercept can be computed by setting y = 0 and z = 0

2x + 3*0 + 4*0 = 12

2x + 0 + 0 = 12

2x = 12

2x / 2 = 12 / 2

x * (2 / 2) = 12 / 2

x * (1) = 12 / 2

x = 12 / 2

x = 6

the x-intercept = 6, or the point (6, 0, 0)



y-intercept can be computed by setting x = 0 and z = 0

2*0 + 3y + 4*0 = 12

0 + 3y + 0 = 12

3y = 12

3y / 3 = 12 / 3

y * (3 / 3) = 12 / 3

y * (1) = 12 / 3

y = 12 / 3

y = 4

the y-intercept = 4, or the point (0, 4, 0)




z-intercept can be computed by setting x = 0 and y = 0

2*0 + 3*0 + 4z = 12

0 + 0 + 4z = 12

4z = 12

4z / 4 = 12 / 4

z * (4 / 4) = 12 / 4

z * (1) = 12 / 4

z = 12 / 4

z = 3

the z-intercept = 3, or the point (0, 0, 3)


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If you were to plot two 3-variable linear equations whose planes intersect, the solution would be the line formed by the intersection of the two planes.

If you were to plot three 3-variable linear equations whose planes intersect, the solution would be that single point where all three planes intersect.






Thanks for writing.

Staff
www.solving-math-problems.com



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