Question

“Two lines which are parallel must have positive slopes”. Explain why you believe this is true or false

Answer 1

Answer: This is false.

Step-by-step explanation:

A linear equation is an equation of the shape.

y = ax + b

where a is the slope, and b is the y-axis intercept.

Two different linear equations are parallel if their slopes are the same, in this case b will define the distance between our two parallel lines.

We do not have any implication on the sign of a, but let's prove this:

Two lines f and g are parallel if there does not exist a value x1 such:

f(x1) = g(x

suppose that f(x) = -ax + b

                     g(x) = -ax + c

where b and c are different numbers (because if b and c are equal, we have that g(x) and f(x) represent the same line)

Now suppose that x1 exists, let's prove that this is absurd.

f(x1) = -ax1 + b = -ax1 + c = g(x1)

b = c

this is absurd, then x1 does not exist and f(x) and g(x) are parallel.

So you can see that the sign of the slope does not matter.

Then the statement is false