Question

Which system of equations is represented by the graph?

Answer 1

Answer:

$\large\boxed{C)\ \left\{\begin{array}{ccc}y=x\\\\y=\dfrac{-x+10}{x-4}\end{array}\right}$

Step-by-step explanation:

We have the points

(-2 , -2) → x = -2 and y = -2 → x = y

(5, 5) → x = 5 and y = 5 → x = y

The equation of a line is $y=x$

The hyperbola has the vertical asymptote x = a and the horizontal asymptote y = -1.

Therefore the second equation is:

$y=\dfrac{a}{x-4}-1=\dfrac{a}{x-4}-\dfrac{x-4}{x-4}=\dfrac{a-(x-4)}{x-4}=\dfrac{a-x+4}{x-4}$

Where a > 0.

The corresponding equation in the solutions to choose is:

$y=\dfrac{-x+10}{x-4}$