The correct reason to substitute $x = 0$ into the equation to find the y-intercept is:

"The y-intercept is the point where the graph intersects the y-axis, and hence the x-coordinate of that point will be 0."

Explanation:

• The y-intercept occurs where the graph crosses the y-axis. By definition, every point on the y-axis has an x-coordinate of 0.
• Therefore, to find the y-intercept, you set $x = 0$ in the equation of the function and solve for $y$. The resulting $y$ value is the y-coordinate of the y-intercept, and the ordered pair $(0, y)$ represents the y-intercept.

Incorrect Statements:

1. "The x-intercept will be 0": This is incorrect because the x-intercept is where the graph crosses the x-axis, not necessarily at 0. The x-intercept is found by setting $y = 0$, not $x = 0$.
2. "The y-intercept is always at (0,0)": This is incorrect because the y-intercept can be any point on the y-axis. It's only $(0, 0)$ if the graph passes through the origin.
3. "The y-intercept is the point where the graph intersects the x-axis and hence the x-coordinate of that point will be 0": This is incorrect because the y-intercept is where the graph intersects the y-axis, not the x-axis.

Would you like more information on how intercepts are calculated or any other related topic?

Here are 5 related questions to consider:

1. How do you find the x-intercept(s) of a graph given its equation?
2. Can a function have multiple y-intercepts? Why or why not?
3. How does changing the slope of a linear function affect the location of the y-intercept?
4. What does the y-intercept tell you about the real-world context in an applied problem?
5. How can you find the y-intercept from a graph without having the equation?

Tip: Understanding the geometric interpretation of intercepts is key in graphing functions and solving equations. The y-intercept is where the graph meets the y-axis, so setting $x = 0$ is the way to find it.