Eq 1 y = 2x + 3
Eq 2 y = 2x + 1
How can you determine these are parallel? Can you graph both equations? Is it possible the lines do intersect somewhere away from the coordinates you are plotting?
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They are parallel because they both have the same coefficient of y, which is the slope. They will never intersect
To determine if two equations are parallel, we need to compare their slopes. In both equations, the coefficient of x is 2. Since the slopes are the same, we can conclude that the lines represented by these equations are indeed parallel.
To graph these equations, we can plot a few points for each and then connect them to create a line.
For equation 1, y = 2x + 3:
- Pick a few values for x, let's use -2, 0, and 2.
- For x = -2: y = 2(-2) + 3 = -1
- For x = 0: y = 2(0) + 3 = 3
- For x = 2: y = 2(2) + 3 = 7
So, we have the points (-2, -1), (0, 3), and (2, 7) for equation 1.
For equation 2, y = 2x + 1:
- Using the same values for x, we can find the corresponding y-values.
- For x = -2: y = 2(-2) + 1 = -3
- For x = 0: y = 2(0) + 1 = 1
- For x = 2: y = 2(2) + 1 = 5
So, we have the points (-2, -3), (0, 1), and (2, 5) for equation 2.
Now, we can plot these points on a graph and draw a line through them.
Regarding the second part of your question, it is not possible for these lines to intersect somewhere away from the coordinates we plotted. Since their slopes are the same and they are straight lines, they will never intersect.