Plotting Points and Graphing Lines in 3-Dimensions

A 3-D coordinate plane looks like this:

where the x-axis comes out towards you, the y-axis is now the horizontal axis, and the z-axis is now the vertical axis. To plot a point in 3-D, you must first go over by your x, then over by your y, then up/down by your z. Your answer might not look like it makes sense - AND THAT'S OKAY! We're trying to graph something in 3-D on a 2-D piece of paper, so naturally, it's not going to look 1005 perfect. Just make sure you get the point in the general correct area of the graph.

To graph a line in 3-D, such as 3x + 4y + 3z = 12, we substitute zeroes in for every variable that we're not trying to find. For example, when trying to find x, I would keep x and plug in 0's for y and z, like this: 3x + 4(0) + 3(0) = 12. The zeroes would cancel out, and when solving for x, divide by 3 on both sides to get x = 4. Plot this on the 3-D plane. Repeat this process for the other two variables and plot them as well. Your final answer should be three points: connect them together and make a triangle, then shade in the triangle to represent the plane of answers.