1. 2/15/20166.5: Lines and Planes in Space No state expectations directly addressed.

2. 2/15/20166.5: Lines and Planes in Space Standard form of an equation for a line: Ax+By=C. Standard form of an equation for a plane: Ax+By+Cz=D.

3. 2/15/20166.5: Lines and Planes in Space x, y, and z intercepts. Just like when graphing on a plane, the intercepts tell us where our graph intersects each axis. The only difference is that now our graph is a plane not a line.

4. 2/15/20166.5: Lines and Planes in Space Graphing a plane by its intercepts: 1.x-intercept: let y and z = 0; solve for x. 2. y-intercept: let x and z = 0; solve for y. 3. z-intercept: let x and y = 0; solve for z. 4. plot the points and connect them, forming a plane.

5. 2/15/20166.5: Lines and Planes in Space Determine the x,y, and z intercepts for 4x +2y +6z = 12.

6. 2/15/20166.5: Lines and Planes in Space Graph 4x +2y + 6z = 12 using its intercepts.

7. 2/15/20166.5: Lines and Planes in Space Graph 3x – 5y+ 3z = 15

8. 2/15/20166.5: Lines and Planes in Space Graph 3x – 2z = 6 in space. An equation with 2 variables in space is still a plane.

9. 2/15/20166.5: Lines and Planes in Space Trace of a Plane The trace of a plane is the intersection of a given plane and the xy-plane. The trace of a plane is a line. To find the equation of the trace, let z = 0 and solve.

10. 2/15/20166.5: Lines and Planes in Space Find the equation of the trace for the plane determined by 3x-6y - 4z = 12. Then sketch the plane and indicate the trace.

11. 2/15/20166.5: Lines and Planes in Space 3x-6y - 4z = 12

12. 2/15/20166.5: Lines and Planes in Space Graph the line determined by x=2t y=4t-2

13. 2/15/20166.5: Lines and Planes in Space Parametric Equations In parametric equations, the expressions for each variable are given in terms of some variable such as time (t). The previous example was an example of parametric equations.

14. 2/15/20166.5: Lines and Planes in Space Plot the line for the parametric equations: x = t+1 y = 2t z = 3t – 4

15. 2/15/20166.5: Lines and Planes in Space

16. 2/15/20166.5: Lines and Planes in Space Plot the line for the parametric equations: x = t y = 2t -1 z = t + 3

17. 2/15/20166.5: Lines and Planes in Space

18. 2/15/20166.5: Lines and Planes in Space Write parametric equations to describe a line that goes through (2,4,6) and (3,6,9). t xt yat + b zct + d

19. 2/15/20166.5: Lines and Planes in Space Write a set of parametric equations to describe a line that goes through (4,12,-7) and (6,16,-9).

20. 2/15/20166.5: Lines and Planes in Space Assignment pages 405-406, #14-38 (evens)