Answer:
[tex] (A)\displaystyle \begin{array} {ccc} \displaystyle y = - 2 \\ x - 2y = 6\\ \end{array} [/tex]
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
[tex] \displaystyle \large y = - 2[/tex]
Equation of the red line:
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]
