I have an understanding problem that I need to clarify..
The equation of line $L$ is $2y = -5x + 10$. A point $P$ lies on the line such that its "distance from the $x$ axis is twice that of its distance from the $y$ axis". Find the coordinates of $P$.
For the sentence that I quoted above ...
Why is the equation for that sentence: $y = 2x$
Thanks for your help in advance ..
Technically the equation for the sentence is $|y| = 2|x|$. The equation give you all of the points where the distance to the x axis is twice the distance to the y axis. $|x|$ is distance to the y axis. If you imagine drawing a line straight from the y axis to some point then the length of that line will be the x coordinate of the point. The same is true for the x axis except $|y|$ is the distance.
To find the point (or points since there may be more than on answer) you have to find the points where the statement $|y| = 2|x|$ is true and that happen to lie on the line $2y = -5x + 10$. You have have a system of two equations with two variables that you can solve using one of the methods that you have been taught.