Find the Intersection Point of a Line and Plane: Step by Step Guide

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To find the intersection point of the given line and plane, start by substituting the line's equations x = -4t + 4, y = -4t + 6, and z = 5t + 5 into the plane equation 4x - 2y + 6z = 78. This substitution will yield a linear equation in terms of t. Solve this equation for t, then use the value of t to calculate the corresponding x, y, and z coordinates from the line's equations. This process will provide the intersection point of the line and the plane. Following these steps will ensure the solution is accurate.
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coordinate help please :)

Hi i just got my home work but don't know where to start. Any help on this just to get me started would be great:) I want to make sure I am doing it right

Thank you


Work out the coordinates where this line meets this plane.

Line x = -4 t + 4, y = -4 t + 6, z = 5 t + 5 and plane 4 x - 2 y + 6 z = 78.
 
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Plug your expressions for x,y,z into the plane definition. You now have an equation (linear) for t. Solve for t and plug it into your x,y,z definitions for the line.
 
hey thank you for replying i will give that a go :)
 

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