line with x -intercept of 3 and y -intercept of -2

To find the equation of a line with a given \(x\)-intercept and \(y\)-intercept, we can use the intercept form of a line's equation:

\[
\frac{x}{a} + \frac{y}{b} = 1
\]

Where:
- \(a\) is the \(x\)-intercept,
- \(b\) is the \(y\)-intercept.

Given:
- \(x\)-intercept \(a = 3\),
- \(y\)-intercept \(b = -2\).

Substituting these values into the equation:

\[
\frac{x}{3} + \frac{y}{-2} = 1
\]

To express this equation in a standard linear form \(Ax + By = C\), we can multiply both sides by the least common multiple of the denominators, which is 6:

\[
2x - 3y = 6
\]

So, the equation of the line is:

\[
2x - 3y = 6
\]

### Do you have any questions or want more details on this?

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Here are 5 related questions you might be interested in:

1. How do you find the slope of the line given its intercepts?
2. What is the general form of a line equation, and how does it relate to slope-intercept form?
3. How would you find the equation of a line parallel to this one through a different point?
4. What is the significance of the intercepts in a real-world context?
5. How do you convert between different forms of linear equations?

**Tip:** When dealing with linear equations, always try to simplify them into a standard form for easier interpretation and comparison.

Learn how to find the equation of a line with a given x-intercept of 3 and y-intercept of -2 using the intercept form and standard form of a linear equation. This problem involves basic concepts of linear equations and is suitable for students in Grades 7-9.

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