Question

The diagram shows two straight lines. Both lines intersect at point A. У y = 4x A х A y = -2 Identify the coordinates of point A. (3-2) (-2,-5) , -8 (-2,2) () (2-2 ) A B D​

Answer 1

Point
`A` is at
`(-1/2,\, -2)`.

Explanation:

The intersection
`(x,\, y)` of two lines in a plane could be found by solving a linear system of two unknowns (
`x` and
`y`) and two equations (one for each line.)

In this question, the equation of the two lines are
`y = 4\, x` and
`y = -2`, respectively. The corresponding system of equations would be:

`\left\lbrace \begin{aligned} & y = 4\, x \\ & y = -2\end{aligned} \right.`.

Solve this system for
`x` and
`y`:

• 
  `y = (-2)`.
• Substitute
  `y = (-2)` into the first equation and solve for
  `x\!`:
  `x = (-1/2)`.

Therefore:

`\left\lbrace \begin{aligned} & x = -(1)/(2) \\ & y = -2\end{aligned} \right.`.

Thus, the coordinates of this intersection
`(x,\, y)` would be
`(-1/2,\, -2)`.