Let's go through this problem.

The line $y = mx$ intersects the y-axis at the origin, point $(0, 0)$. This is because there is no constant term in the equation, so the line passes through the origin.

Now, consider the line $y = mx + 2$. Here, the constant term $+2$ indicates a vertical shift. Specifically, it shifts the entire line $y = mx$ up by 2 units. This means that every point on the line $y = mx$ is now 2 units higher on the y-axis in the line $y = mx + 2$.

Answer

The correct answer is:

• B. The line has been shifted up 2 units.

Would you like a further breakdown or have any questions?

Here are some related questions:

1. What is the significance of the constant term in a linear equation like $y = mx + c$?
2. How does changing the slope $m$ affect the graph of the line?
3. What would the graph of $y = mx - 2$ look like in relation to $y = mx$?
4. How can you determine the y-intercept of a line just by looking at its equation?
5. If the line were shifted left or right, what changes would occur in the equation?

Tip: In linear equations, the y-intercept represents the point where the line crosses the y-axis, and it directly reflects any vertical shift.