Question

which system or equation is represented in the graph?

(A) y=-2
x-2y=6


(B) y=-2
x+2y=6



(C) y=-2
2×-y=3



(D) y=-2
2×+y=-3

​

Answer 1

Answer:

$(A)\displaystyle \begin{array} {ccc} \displaystyle y = - 2 \\ x - 2y = 6\\ \end{array}$

Step-by-step explanation:

Equation of the blue line:

since the line is horizontal and passes -2 the equation of the blue line should be

$\displaystyle \large y = - 2$

Equation of the red line:

remember The form of equation of a line

$\displaystyle \boxed{ \displaystyle y = mx + b}$

where m is slope of the line and b is the y-intercept we can clearly see that the red line crosses y-axis at (0,-3) therefore b=-3

to figure out m we can consider the following formula:

$\displaystyle m = \frac{ \Delta y}{ \Delta x}$

from the graph we acquire ∆y=1 and ∆x=2

thus substitute:

$\displaystyle m = \frac{ 1}{ 2}$

so we have figured out m and b

therefore our equation of blue line is

$\displaystyle y = \frac{1}{2} x - 3$

our given options are in standard form so

move -3 to left hand side and change its sign:

$\displaystyle y + 3= \frac{1}{2} x$

cross multiplication:

$\displaystyle 2y + 6= x$

move 6 to right hand side and x to left hand side and change its sign

$\displaystyle - x + 2y = - 6$

multiply both sides by -1:

$\displaystyle x - 2y = 6$

hence, our system of linear equation is

$\displaystyle \begin{cases} \displaystyle y = - 2 \\ x - 2y = 6\\ \end{cases}$