Graph the two linear equations in each system on a singular coordinate plane and state whether the lines are intersecting, para or the same line
Y= 4 - 2x
Y= -2x + 4
To graph the two linear equations, we can start by determining their slopes and y-intercepts.
The first equation, Y = 4 - 2x, is in slope-intercept form (Y = mx + b) where the slope (m) is -2 and the y-intercept (b) is 4.
The second equation, Y = -2x + 4, is also in slope-intercept form where the slope is -2 and the y-intercept is 4.
Since both equations have the same slope (-2) and y-intercept (4), we can conclude that the lines are the same.
To graph the lines, we can plot a few points for each equation and draw a straight line passing through those points.
For the first equation, Y = 4 - 2x:
Let's choose two x-values and find the corresponding y-values.
When x = 0, Y = 4 - 2(0) = 4.
When x = 2, Y = 4 - 2(2) = 0.
So, we have two points (0, 4) and (2, 0) for the first equation.
For the second equation, Y = -2x + 4:
Again, let's choose two x-values and find the corresponding y-values.
When x = 0, Y = -2(0) + 4 = 4.
When x = 2, Y = -2(2) + 4 = 0.
So, we have two points (0, 4) and (2, 0) for the second equation as well.
Since the points for both equations are the same, we can represent them as a single line on a coordinate plane.
The graph of both equations will be a straight line passing through the points (0, 4) and (2, 0). The line goes downwards from left to right, indicating that the slope is negative.
In conclusion, the lines are the same.