Show me a graph of a liner equation -2x+y=6 and 4x-2y=-12

Answer 1

To plot a graph for each equation, we first need to rearrange them in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

1) -2x + y = 6
Adding 2x to both sides, we get:
y = 2x + 6

2) 4x - 2y = -12
Dividing both sides by -2, we get:
-2x + y = 6
y = 2x - 6

Now we can graph these equations:

Graph of -2x + y = 6:
The slope (m) is 2, and the y-intercept (b) is 6.
Start by plotting the y-intercept of (0,6), then use the slope to find the next point.
From (0,6), move 1 unit to the right and 2 units up. Plot this second point and draw a straight line through both points.

Graph of 4x - 2y = -12:
Divide the equation by -2 to obtain y = 2x - 6.
The slope (m) is also 2 and the y-intercept (b) is -6.
Start by plotting the y-intercept of (0,-6), then use the slope to find the next point.
From (0,-6), move 1 unit to the right and 2 units up. Plot this second point and draw a straight line through both points.

Here is the graph of the two equations on the same coordinate system:

Graph of the equations -2x + y = 6 (in blue) and 4x - 2y = -12 (in red):