Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To determine which equation represents a street parallel to the given line [tex]\( -7x + 3y = -21.5 \)[/tex], we need to follow these steps:
1. Identify the Ratio of the Coefficients:
The equation of the given street [tex]\( -7x + 3y = -21.5 \)[/tex] can be compared to the standard linear form [tex]\( Ax + By = C \)[/tex]. The coefficients of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are [tex]\( -7 \)[/tex] and [tex]\( 3 \)[/tex], respectively.
2. Calculate the Ratio for the Given Line:
The ratio of the coefficients of [tex]\( x \)[/tex] to [tex]\( y \)[/tex] in the given line is:
[tex]\[ \frac{-7}{3} \][/tex]
3. Determine the Ratios for the Option Lines:
Let's now compare this ratio with the coefficients in the given options:
- Option A: [tex]\( -3x + 4y = 3 \)[/tex]
The coefficients are [tex]\( -3 \)[/tex] for [tex]\( x \)[/tex] and [tex]\( 4 \)[/tex] for [tex]\( y \)[/tex]. The ratio is:
[tex]\[ \frac{-3}{4} \][/tex]
- Option B: [tex]\( 3x + 7y = 63 \)[/tex]
The coefficients are [tex]\( 3 \)[/tex] for [tex]\( x \)[/tex] and [tex]\( 7 \)[/tex] for [tex]\( y \)[/tex]. The ratio is:
[tex]\[ \frac{3}{7} \][/tex]
- Option C: [tex]\( 2x + y = 20 \)[/tex]
The coefficients are [tex]\( 2 \)[/tex] for [tex]\( x \)[/tex] and [tex]\( 1 \)[/tex] for [tex]\( y \)[/tex]. The ratio is:
[tex]\[ \frac{2}{1} \text{ or simply } 2 \][/tex]
- Option D: [tex]\( 7x + 3y = 70 \)[/tex]
The coefficients are [tex]\( 7 \)[/tex] for [tex]\( x \)[/tex] and [tex]\( 3 \)[/tex] for [tex]\( y \)[/tex]. The ratio is:
[tex]\[ \frac{7}{3} \][/tex]
4. Compare the Ratios:
We need to compare each of these ratios to the ratio of the given line [tex]\( \frac{-7}{3} \)[/tex]:
- [tex]\( \frac{-3}{4} \neq \frac{-7}{3} \)[/tex]
- [tex]\( \frac{3}{7} \neq \frac{-7}{3} \)[/tex]
- [tex]\( \frac{2}{1} \neq \frac{-7}{3} \)[/tex]
- [tex]\( \frac{7}{3} \)[/tex] matches the negative of [tex]\( \frac{-7}{3} \)[/tex]. Moreover, [tex]\( \frac{7}{3} \)[/tex] is the positive version which signifies parallelism, as parallel lines have the same gradient (magnitude of the ratio) even if they differ in sign.
5. Conclusion:
The equation of the line parallel to the given line [tex]\( -7x + 3y = -21.5 \)[/tex] is:
[tex]\[ \boxed{7x + 3y = 70} \][/tex]
Option D correctly represents the equation of the central street [tex]\( PQ \)[/tex].
1. Identify the Ratio of the Coefficients:
The equation of the given street [tex]\( -7x + 3y = -21.5 \)[/tex] can be compared to the standard linear form [tex]\( Ax + By = C \)[/tex]. The coefficients of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are [tex]\( -7 \)[/tex] and [tex]\( 3 \)[/tex], respectively.
2. Calculate the Ratio for the Given Line:
The ratio of the coefficients of [tex]\( x \)[/tex] to [tex]\( y \)[/tex] in the given line is:
[tex]\[ \frac{-7}{3} \][/tex]
3. Determine the Ratios for the Option Lines:
Let's now compare this ratio with the coefficients in the given options:
- Option A: [tex]\( -3x + 4y = 3 \)[/tex]
The coefficients are [tex]\( -3 \)[/tex] for [tex]\( x \)[/tex] and [tex]\( 4 \)[/tex] for [tex]\( y \)[/tex]. The ratio is:
[tex]\[ \frac{-3}{4} \][/tex]
- Option B: [tex]\( 3x + 7y = 63 \)[/tex]
The coefficients are [tex]\( 3 \)[/tex] for [tex]\( x \)[/tex] and [tex]\( 7 \)[/tex] for [tex]\( y \)[/tex]. The ratio is:
[tex]\[ \frac{3}{7} \][/tex]
- Option C: [tex]\( 2x + y = 20 \)[/tex]
The coefficients are [tex]\( 2 \)[/tex] for [tex]\( x \)[/tex] and [tex]\( 1 \)[/tex] for [tex]\( y \)[/tex]. The ratio is:
[tex]\[ \frac{2}{1} \text{ or simply } 2 \][/tex]
- Option D: [tex]\( 7x + 3y = 70 \)[/tex]
The coefficients are [tex]\( 7 \)[/tex] for [tex]\( x \)[/tex] and [tex]\( 3 \)[/tex] for [tex]\( y \)[/tex]. The ratio is:
[tex]\[ \frac{7}{3} \][/tex]
4. Compare the Ratios:
We need to compare each of these ratios to the ratio of the given line [tex]\( \frac{-7}{3} \)[/tex]:
- [tex]\( \frac{-3}{4} \neq \frac{-7}{3} \)[/tex]
- [tex]\( \frac{3}{7} \neq \frac{-7}{3} \)[/tex]
- [tex]\( \frac{2}{1} \neq \frac{-7}{3} \)[/tex]
- [tex]\( \frac{7}{3} \)[/tex] matches the negative of [tex]\( \frac{-7}{3} \)[/tex]. Moreover, [tex]\( \frac{7}{3} \)[/tex] is the positive version which signifies parallelism, as parallel lines have the same gradient (magnitude of the ratio) even if they differ in sign.
5. Conclusion:
The equation of the line parallel to the given line [tex]\( -7x + 3y = -21.5 \)[/tex] is:
[tex]\[ \boxed{7x + 3y = 70} \][/tex]
Option D correctly represents the equation of the central street [tex]\( PQ \)[/tex].
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
