First of all, is it Geometric?
Image of the drafted:
I need help solving this question, and I am completely lost on how can I solve this. Could anyone explain the way of solving this geometric question?
Here is a drafting of the two lines I and II. With 3 formulas (a), (b), (c).
(a) $y = 2x + 8$,
(b) $y = - 2x + 8$
(c) $y = x + 2$.
A. Every of the straights I and II, please find the correct formula out of the formulas (a) , (b) , (c), and explain your answer.
b. Find the points of intersection of the straight rates.
c. Find the straight formula that's going through the way of the point (5, 2) and parallels to the straight II.
How do I do this?
This is a translated version.
Hints: for the straight line $\,y=ax+b\,$:
$\bullet\;\;$ The line above is ascending iff $\,a>0\,$ , and it is constant iff $\,a=0\,$ ;
$\bullet\;\;$ the $\,y$-intersection of the above line is the point $\,(0,b)\,$ ;
$\bullet\;\;$ The line above intercepts the line $\,y=mx +n\,$ at the point $\,(x_0,y_0)\,$ which is the solution of the linear system
$$\begin{cases}y=ax+b\\{}\\y=mx+n\end{cases}$$
How to solve: compare $\,y$-s:
$$ax+b=mx+n\implies(a-m)x=n-b\implies \,\text{if}\;a\neq b\;,\;x=\frac{n-b}{a-m}$$
Iff $\,a=b\,$ the lines are parallel and thus they are the very same line or else they have no common point.