When a student sets y=0 into a linear equation, she can solve for x and gets x=-3. When she sets x=0 and solves the equation, she gets y=4. Which of the following is the correct statement of the intercepts and graph?

*x*-intercept: (-3,0)

*y*-intercept: (0,4)

*x*-intercept: (-3,0)

*y*-intercept: (0,4) 

*x*-intercept: (0,-3)

*y*-intercept: (4,0) 

*x*-intercept: (-3,0)

*y*-intercept: (4,0)


The correct statement of the intercepts is:

- **x-intercept**: \((-3,0)\)
- **y-intercept**: \((0,4)\)

This matches the first option in the list:

- **x-intercept**: \((-3,0)\)
- **y-intercept**: \((0,4)\)

This means that when \( y = 0 \), the point on the x-axis is \((-3, 0)\), and when \( x = 0 \), the point on the y-axis is \((0, 4)\).

Would you like more details or have any questions?

Here are 5 related questions to explore this further:
1. How do you derive the equation of a line using the intercepts?
2. What is the slope of the line passing through the points \((-3, 0)\) and \((0, 4)\)?
3. How do x- and y-intercepts help in graphing linear equations?
4. Can a linear equation have more than one x- or y-intercept?
5. How do the intercepts change if you multiply the entire equation by a constant?

**Tip**: You can use the intercepts to quickly sketch the line, as they tell you where the line crosses the axes!

When a student sets y=0 into a linear equation, she can solve for x and gets x=-3. When she sets x=0 and solves the equation, she gets y=4. Which of the following is the correct statement of the intercepts and graph?

Explore how to identify x- and y-intercepts in linear equations with a step-by-step example. This problem helps students understand coordinate geometry, including solving for intercepts, and is suitable for Grades 8-10.

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