
Write the general equation of the line that has an x-int at 4 and a y-int at 2.

To find the general equation of the line with an x-intercept at \(4\) and a y-intercept at \(2\), we can use the intercept form of the equation of a line:

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

where \(a\) is the x-intercept and \(b\) is the y-intercept.

Given:
- \(a = 4\) (x-intercept)
- \(b = 2\) (y-intercept)

Substitute these values into the equation:

\[
\frac{x}{4} + \frac{y}{2} = 1
\]

To express this in the general form \(Ax + By + C = 0\), we can multiply through by the least common multiple (LCM) of the denominators, which is \(4\):

\[
\frac{4x}{4} + \frac{4y}{2} = 4
\]

Simplifying:

\[
x + 2y = 4
\]

Now, to put it in the general form:

\[
x + 2y - 4 = 0
\]

So, the general equation of the line is:

\[
\boxed{x + 2y - 4 = 0}
\]

Would you like to explore more details on this, or do you have any questions?

Here are 5 related questions you might find interesting:
1. How do you find the slope of the line from the general form equation?
2. What is the equation of a line parallel to this one but passing through the point \((1, 3)\)?
3. How do you convert the equation from general form to slope-intercept form?
4. What is the distance from the origin to the line given by this equation?
5. How do you find the equation of a line perpendicular to this one?

**Tip:** Remember that the general form of a line \(Ax + By + C = 0\) is very flexible; you can quickly find the slope and intercepts by manipulating it into different forms.

Write the general equation of the line that has an x-int at 4 and a y-int at 2.

Learn how to derive the general equation of a line with an x-intercept of 4 and a y-intercept of 2. This problem covers important algebraic concepts such as intercept form and general form of linear equations, making it ideal for students in Grades 9-10.

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