Question 161588: I am having a very hard time understanding this, can you please help?
Determine whether the graphs of the pair of lines are parallel.
x+13=y
y-x=-9
For x+13=y, I came up with the answer x-y+13=0 but I am not sure if it is right and why or why not.
For y-x=-9, I came up with the answer of -8; again I am not sure.
What is the slope of the line x+13=y?
What is the slope of the line y-x=-9?
Are the graphs of the equations parallel?
Found 2 solutions by checkley77, nerdybill:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! x+13=y
y-x=-9
The first thing you must do is find the slope (m) by placing these formula in the standard line form:
Y=mX+b where x & y are a set of graph points, m=slope (y2-y1)/(x2-x1) & b=the y intercept.
y=x+13 This line has a slope (m)=1. (red line)
y=x-9 This line also has a slope (m)=1. (green line)
Therefore they are parallel lines.
Proof:
 (graph 300x200 pixels, x from -16 to 15, y from -10 to 15, of TWO functions x +13 and x -9).
Answer by nerdybill(7384)  (Show Source):
You can put this solution on YOUR website! The idea is to convert each equation into the "slope-intercept" form of a line:
y = mx + b
where
m is slope
b is y-intercept at (0,b)
.
Once you do that, it is easy to identify the slope.
.
1st equation (is already there just rearrange):
x+13=y
y = x + 13
or, you can write:
y = (1)x + 13
Now, you can see that the slope of equation 1:
m = 1
.
2nd equation:
y-x=-9
move the x to right by adding x to both sides:
y = x-9
again, you can write:
y = (1)x-9
Now, you can see that the slope of equation 2:
m = 1
.
If two lines are parallel, their slopes must be the same. Since both equations have the same slope of 1, the two equations are parallel.
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