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:

[tex] (A)\displaystyle \begin{array} {ccc} \displaystyle y = - 2 \\ x - 2y = 6\\ \end{array} [/tex]

Step-by-step explanation:

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

[tex] \displaystyle \large y = - 2[/tex]

remember The form of equation of a line

[tex] \displaystyle \boxed{ \displaystyle y = mx + b}[/tex]

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:

[tex] \displaystyle m = \frac{ \Delta y}{ \Delta x} [/tex]

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

thus substitute:

[tex] \displaystyle m = \frac{ 1}{ 2} [/tex]

so we have figured out m and b

therefore our equation of blue line is

[tex] \displaystyle y = \frac{1}{2} x - 3[/tex]

our given options are in standard form so

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

[tex] \displaystyle y + 3= \frac{1}{2} x [/tex]

cross multiplication:

[tex] \displaystyle 2y + 6= x[/tex]

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

[tex] \displaystyle - x + 2y = - 6[/tex]

multiply both sides by -1:

[tex] \displaystyle x - 2y = 6[/tex]

hence, our system of linear equation is

[tex] \displaystyle \begin{cases} \displaystyle y = - 2 \\ x - 2y = 6\\ \end{cases}[/tex]

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