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

Answer:

(A)y = -2,   x-2y =6.

Step-by-step 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

$=\dfrac{0-(-3)}{6-0} \\=3\div 6 \\=\dfrac{1}{2}$

So we have:

$y=\dfrac{1}{2}x+b$

When x=0, y=-3

$-3=\dfrac{1}{2}(0)+b\\b=-3$

Therefore, the second equation is:

$y=\dfrac{1}{2}x-3\\ Multiplying all through by 2, we have:\\2y=x-6$

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.