Help, Parametric and vector eqns of a lines

[saady87]

well, I am lost...im not sure if this goes in college or k-12, but I am in grade 12 in Canada...and I am learning here, so i guess I am at the right place,
any wyas...i need help, with parametric and vector eqns of lines, since I am failing this course horribly...my teacher sucks and marks hard and I don't get anything!...
so now for the questions

The angle ø, 0° < ø < 180°, That a line makes with the positive x-axis is called the angle of inclination of hte line.

A) find the angel of inclination of each of hte following lines.
_
i) r = (2,-6) + t(3,-4) ii) r = (6,1) + t(5,1)

B) prove that the tange of the angle of inclination is equal to the slope of hte line.

 

[robphy]

Here's a related thread
https://www.physicsforums.com/showthread.php?t=49212

Slope of line= rise/run
Now, regard the rise and run as legs of a right triangle.

 

[saady87]

that didnt help me even a remote bit...still lost...:(

 

[robphy]

Plot r(t) on a graph (t along the horizontal axis, r along the vertical axis).
Choose two values of t (say t=0 and t=1)
Evaluate r at t=0. That gives you a point P with coordinates (t,r)=( 0, r(0) ).
Evaluate r at t=1. That gives you a point Q with coordinates (t,r)=( 1, r(1) ).
Calculate the slope of the line segment PQ.

Now think of PQ as the hypotenuse of a right triangle,
with one leg parallel to the horizontal t-axis
and the other leg parallel to the vertical r-axis.
The angle of inclination is an angle of that triangle.
Use trigonometry to relate that angle to your triangle legs and the slope.