Question

Do all lines with the same slope have the same line?

Answer 1

No, not all lines with the same slope have the same line.

If they're y and/or x intercepts are different then they could have the same slope, but not have the same line.

Here's an example:
The equation for a linear line is y = mx + b
Where m = the slope and b = the y intercept.

If we have two lines y = 2x + 1 and y = 2x + 10, they both have the same slope, but they are different lines:

If they are the same line: I should be able to plug one x value into both equations and I would get the same value, but if they are different then I won't get the same y value for each x value.

ex: if x = 2
y = 2x + 1 => y = 2(2) + 1 => y = 5
y = 2x + 10 => y = 2(2) + 10 => y = 14

As you can see I plugged in the same x value into both equations (they have same slope) and I got different values.

Hope this answers your question!

-Jabba

Answer 2

No, not necessarily. They could have different y intercepts.

For example, take one horizontal line, and another horizontal line.

These horizontal lines would both have the same slope, 0. But one could be higher up, or have a higher y intercept, than the other.

They would still have the same slope, but not be the same line.