A line with an inclination passes through (-5/2, -9/2), what is the x-coordinate of a point on the line if its corresponding y-coordinate is 6?

Question

A line with an inclination passes through (-5/2, -9/2), what is  the x-coordinate of a point on the line if its corresponding y-coordinate is 6?

anonymous · Answer

@Michele_Laino  can you help me? :)

michele_laino · Answer

if we write the line3 as below:
$$\Large  ax + by + c = 0$$
we get, by substitution:
$$\Large  2c = 5a + 9b$$
next I substitute $y=6$ into the first equation:
$$\Large  a{x_0} + 6b + c = 0$$
then I substitute $c$:
$$\Large  a\left( {{x_0} + 5} \right) + 15b = 0$$

anonymous · Answer

why did you put (Xo + 5 )?

anonymous · Answer

@Michele_Laino

michele_laino · Answer

sorry I have made an error.
If I substitute the value for $c$, I get:
$$\Large   \begin{gathered}
  a{x_0} + 6b + \frac{{5a + 9b}}{2} = 0 \hfill \
   \hfill \
  2a{x_0} + 12b + 5a + 9b = 0 \hfill \
   \hfill \
  a\left( {2{x_0} + 5} \right) + 21b = 0 \hfill \ 
\end{gathered} $$

michele_laino · Answer

where $x_0$ is the requested x-coordinates

michele_laino · Answer

x-coordinate*

anonymous · Answer

then what should i do?  i'm sorry :(

michele_laino · Answer

I also don't know
I think that we need to know another quantity, for example, the slope of the line

michele_laino · Answer

for example, do the line pass at the origin $(0,0)$

michele_laino · Answer

does*