Does x=4y+1 and x=4y-1 equal the same thing?
I have a math problem for my class asking this question,
and I am supposed to explain it to someone new to math.
I am so confused about it though, that I cannot explain it to anyone.
No, they don't equal the same thing. They are the equations for
two lines. They are parallel, one crossing the y-axis above the
x-axis, the other crossing the y-axis below the x-axis.
Re-work the equations so that the y term is on the left
side of the equation.
First one:
x = 4y + 1
x - 4y = 1
-4y = -x + 1
y = 1/4 x - 1/4
Second one:
x = 4y - 1
x - 4y = -1
-4y = -x - 1
y = 1/4 x + 1/4
Why are they parallel? Both of them have a
slope of 1/4. How do we know that one crosses
the y-axis above the x-axis and the other crosses
below the x-axis? The y-intercept in one equation
is positive 1/4; the y-intercept in the other equation
is negative 1/4.