The graph of which of the following lines contains the point (5,0) and makes an angle of 45 degrees with the positive x-axis?
Now the solution is y=x-5 but why couldn't the solution be y=(3x-15)/2 or y=2x+10?? I guess I'm stuck on the the 45 degree part..
It is because it has been proven.
We know from coordinate geometry that the gradient of a straight line is the rise over run.
Consider the following triangle attached at the bottom of this post:
(Note: the diagonal line is "straight line" whose equation you are looking for)
If the gradient of the diagonal line is symbolised by the letter m
From trigonometry, we know that is also
Therefore
To find the equation of a straight line, you need a point and gradient m.