Question

Which system of equations is represented in the graph? On a coordinate plane, a horizontal line is at y = negative 2 and another line goes through (0, negative 3) and (6, 0). y = negative 2. x minus 2 y = 6. y = negative 2. x + 2 y = 3. x = negative 2. 2 x minus y = 3. x = negative 2. 2 x + y = negative 3.

Answer 1

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

Explanation:

On the graph, we have two lines:

• y = -2
• The line that goes through (0, -3) and (6, 0).

To determine the equation of the second line, we use the slope-intercept form: y=mx+b

Slope, m

`=(0-(-3))/(6-0) \\=3/ 6 \\=(1)/(2)`

So we have:

`y=(1)/(2)x+b`

When x=0, y=-3

`-3=(1)/(2)(0)+b\\b=-3`

Therefore, the second equation is:

`y=(1)/(2)x-3\\$Multiplying all through by 2, we have:\\2y=x-6`

Rearranging: x-2y=6

The system of equations that is represented in the graph is:

• y = -2.
• x-2y =6.

The correct option is A.