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

Answer:

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

Step-by-step 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:

$\left\lbrace \begin{aligned} & x = -\frac{1}{2} \\ & y = -2\end{aligned} \right.$.

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