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

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

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 = ( \Delta y)/( \Delta x)`

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

thus substitute:

`\displaystyle m = ( 1)/( 2)`

so we have figured out m and b

therefore our equation of blue line is

`\displaystyle y = (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= (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}`