1. ## Graphing an equation

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..

2. Originally Posted by donnagirl
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..
Formula: $m = \tan \theta$ where $\theta$ is the angle the line makes with the positive x-axis.

3. Still am not sure...do you mean "m" is the slope?? And also why does it have to be tangent? Why not sin or cos?

4. It is $tan \;\theta$ 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

$m = \frac {rise}{run}$

$= \frac {opposite}{adjacent}$
From trigonometry, we know that $\frac {opposite}{adjacent}$ is also $tan \;\theta$

Therefore $m = tan\;\theta$

To find the equation of a straight line, you need a point $(x_1,y_1)$ and gradient m.