If we are asked to to find the y-intercept of the graph given its equation, we substitute x=0 into the equation, because:



The x-intercept will be 0

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

The y-intercept is always at (0,0)

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

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.

Discover how to find the y-intercept of a graph using mathematical equations. Learn why substituting x=0 is crucial in determining where the graph intersects the y-axis. This explanation covers key geometric interpretations and common misconceptions about intercepts. Suitable for Grades 7-9 students.

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