Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Alright, let's work through the steps to find the equation of the line in standard form, given that it has [tex]\( x \)[/tex]-intercept [tex]\((-P, 0)\)[/tex] and [tex]\( y \)[/tex]-intercept [tex]\((0, R)\)[/tex].
1. Identify intercepts:
- [tex]\( x \)[/tex]-intercept: [tex]\((-P, 0)\)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\((0, R)\)[/tex]
2. Form of the line equation using intercepts:
- The intercept form of the line equation is given by:
[tex]\[ \frac{x}{a} + \frac{y}{b} = 1 \][/tex]
Where [tex]\( a \)[/tex] is the [tex]\( x \)[/tex]-intercept and [tex]\( b \)[/tex] is the [tex]\( y \)[/tex]-intercept.
3. Substitute intercepts into the intercept form:
- Here, [tex]\( a = -P \)[/tex] and [tex]\( b = R \)[/tex]. So the equation becomes:
[tex]\[ \frac{x}{-P} + \frac{y}{R} = 1 \][/tex]
4. Clear the denominators by multiplying through by [tex]\(-PR\)[/tex]:
- Multiply the entire equation by [tex]\(-PR\)[/tex] to remove the fractions:
[tex]\[ -R \cdot \frac{x}{-P} + P \cdot \frac{y}{R} = -PR \][/tex]
5. Simplify the equation:
- Simplify each term to get a standard form linear equation:
[tex]\[ (-R \cdot \frac{x}{-P}) + (P \cdot \frac{y}{R}) = -PR \][/tex]
[tex]\[ \left( \frac{R}{P} \right) x + \left( \frac{P}{R} \right) y = -PR \][/tex]
- Note that the terms simplify to:
[tex]\[ \frac{R}{P} \cdot x + \frac{P}{R} \cdot y = -PR \][/tex]
[tex]\[ R x - P y = PR \][/tex]
6. Rewrite in standard form:
- Transform and rearrange to get:
[tex]\[ Px - Ry = PR \][/tex]
Therefore, the equation of the line in standard form is:
[tex]\[ P x - R y = P R \][/tex]
This matches the fourth option in the provided list:
[tex]\[ \boxed{P x - R y = P R} \][/tex]
1. Identify intercepts:
- [tex]\( x \)[/tex]-intercept: [tex]\((-P, 0)\)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\((0, R)\)[/tex]
2. Form of the line equation using intercepts:
- The intercept form of the line equation is given by:
[tex]\[ \frac{x}{a} + \frac{y}{b} = 1 \][/tex]
Where [tex]\( a \)[/tex] is the [tex]\( x \)[/tex]-intercept and [tex]\( b \)[/tex] is the [tex]\( y \)[/tex]-intercept.
3. Substitute intercepts into the intercept form:
- Here, [tex]\( a = -P \)[/tex] and [tex]\( b = R \)[/tex]. So the equation becomes:
[tex]\[ \frac{x}{-P} + \frac{y}{R} = 1 \][/tex]
4. Clear the denominators by multiplying through by [tex]\(-PR\)[/tex]:
- Multiply the entire equation by [tex]\(-PR\)[/tex] to remove the fractions:
[tex]\[ -R \cdot \frac{x}{-P} + P \cdot \frac{y}{R} = -PR \][/tex]
5. Simplify the equation:
- Simplify each term to get a standard form linear equation:
[tex]\[ (-R \cdot \frac{x}{-P}) + (P \cdot \frac{y}{R}) = -PR \][/tex]
[tex]\[ \left( \frac{R}{P} \right) x + \left( \frac{P}{R} \right) y = -PR \][/tex]
- Note that the terms simplify to:
[tex]\[ \frac{R}{P} \cdot x + \frac{P}{R} \cdot y = -PR \][/tex]
[tex]\[ R x - P y = PR \][/tex]
6. Rewrite in standard form:
- Transform and rearrange to get:
[tex]\[ Px - Ry = PR \][/tex]
Therefore, the equation of the line in standard form is:
[tex]\[ P x - R y = P R \][/tex]
This matches the fourth option in the provided list:
[tex]\[ \boxed{P x - R y = P R} \][/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.