Hello!
The answer is:
B: They have the same slope of 1 and are, therefore, parallel.
Why?
To solve the problem, we must remember that the slope of a line is represented by the coefficient of the linear term (x) or variable.
The coefficient is the number before the variable, for example:
[tex]3X=3*X[/tex]
The coefficient of the example is 3.
So, we are given the lines:
First:
[tex]x-y=-3\\\\y=x+3[/tex]
We can see that the coefficient of the linear term is equal to 1.
Second:
[tex]x-y=1\\\\y=x-1[/tex]
We can see that the coefficient of the linear term is equal to 1.
Hence, we have that both functions have an equal slope of 1, so, the lines are parallel.
The correct option is:
B: They have the same slope of 1 and are, therefore, parallel.
Have a nice day!
Note: I have attached a picture for better understanding. The first function is represented by the red line, and the second function is represented by the blue line.
