Answer:
Point [tex]A[/tex] is at [tex](-1/2,\, -2)[/tex].
Step-by-step explanation:
The intersection [tex](x,\, y)[/tex] of two lines in a plane could be found by solving a linear system of two unknowns ([tex]x[/tex] and [tex]y[/tex]) and two equations (one for each line.)
In this question, the equation of the two lines are [tex]y = 4\, x[/tex] and [tex]y = -2[/tex], respectively. The corresponding system of equations would be:
[tex]\left\lbrace \begin{aligned} & y = 4\, x \\ & y = -2\end{aligned} \right.[/tex].
Solve this system for [tex]x[/tex] and [tex]y[/tex]:
- [tex]y = (-2)[/tex].
- Substitute [tex]y = (-2)[/tex] into the first equation and solve for [tex]x\![/tex]: [tex]x = (-1/2)[/tex].
Therefore:
[tex]\left\lbrace \begin{aligned} & x = -\frac{1}{2} \\ & y = -2\end{aligned} \right.[/tex].
Thus, the coordinates of this intersection [tex](x,\, y)[/tex] would be [tex](-1/2,\, -2)[/tex].
