To find the equation of a line given its [tex]\( x \)[/tex]-intercept and [tex]\( y \)[/tex]-intercept, we can use the intercept form of the line equation.
1. Identify the intercepts:
- The [tex]\( x \)[/tex]-intercept is [tex]\((-P, 0)\)[/tex].
- The [tex]\( y \)[/tex]-intercept is [tex]\((0, R)\)[/tex].
2. Use the intercept form of the line equation:
The intercept form of the line equation is given by:
[tex]\[
\frac{x}{x\text{-intercept}} + \frac{y}{y\text{-intercept}} = 1
\][/tex]
Plugging in the intercepts [tex]\((-P)\)[/tex] for the [tex]\( x \)[/tex]-intercept and [tex]\( R \)[/tex] for the [tex]\( y \)[/tex]-intercept:
[tex]\[
\frac{x}{-P} + \frac{y}{R} = 1
\][/tex]
3. Simplify the equation:
To eliminate the fractions, we can multiply the entire equation by [tex]\(-P \times R\)[/tex]:
[tex]\[
-P \times R \left(\frac{x}{-P} + \frac{y}{R}\right) = -P \times R \times 1
\][/tex]
4. Clearing the denominators:
When we distribute [tex]\(-P \times R\)[/tex] within the parentheses, we get:
[tex]\[
R x - P y = -P R
\][/tex]
5. Compare with given choices:
We compare this derived equation with the provided options:
- [tex]\(R x - P y = -P R\)[/tex]
- [tex]\(R x + P y = P R\)[/tex]
- [tex]\(P x - R y = -P R\)[/tex]
- [tex]\(P x - R y = P R\)[/tex]
The first option exactly matches [tex]\(R x - P y = -P R\)[/tex].
Therefore, the correct equation of the line in standard form is:
[tex]\[
R x - P y = -P R
\][/tex]
So, the correct choice is:
[tex]\[
\boxed{1}
\][/tex]
