Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To find the equation of a line that is parallel to a given line and passes through a specific point, we can follow these steps:
1. Identify the slope of the given line:
- The equation of the given line is [tex]\( y - 1 = -\frac{3}{2}(x + 3) \)[/tex].
- By comparing this equation with the point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], we see that the slope [tex]\( m \)[/tex] of the given line is [tex]\( -\frac{3}{2} \)[/tex].
2. Determine the slope of the parallel line:
- Lines that are parallel have the same slope. Therefore, the slope of the line parallel to the given line is also [tex]\( -\frac{3}{2} \)[/tex].
3. Use the point-slope form of the equation to find the equation of the parallel line passing through the point [tex]\((-3,1)\)[/tex]:
- The point-slope form is given by [tex]\( y - y_1 = m(x - x_1) \)[/tex].
- Here, [tex]\( m = -\frac{2}{3} \)[/tex], [tex]\( x_1 = -3 \)[/tex], and [tex]\( y_1 = 1 \)[/tex].
4. Substitute the values into the point-slope form:
- Using the given point [tex]\((-3,1)\)[/tex]:
[tex]\[ y - 1 = -\frac{2}{3}(x - (-3)) \][/tex]
- Simplifying the expression inside the parentheses:
[tex]\[ y - 1 = -\frac{2}{3}(x + 3) \][/tex]
Therefore, the equation of the line that is parallel to the given line and passes through the point [tex]\((-3,1)\)[/tex] is:
[tex]\[ y - 1 = -\frac{2}{3}(x + 3) \][/tex]
The correct answer is:
[tex]\[ y-1=-\frac{2}{3}(x+3) \][/tex]
1. Identify the slope of the given line:
- The equation of the given line is [tex]\( y - 1 = -\frac{3}{2}(x + 3) \)[/tex].
- By comparing this equation with the point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], we see that the slope [tex]\( m \)[/tex] of the given line is [tex]\( -\frac{3}{2} \)[/tex].
2. Determine the slope of the parallel line:
- Lines that are parallel have the same slope. Therefore, the slope of the line parallel to the given line is also [tex]\( -\frac{3}{2} \)[/tex].
3. Use the point-slope form of the equation to find the equation of the parallel line passing through the point [tex]\((-3,1)\)[/tex]:
- The point-slope form is given by [tex]\( y - y_1 = m(x - x_1) \)[/tex].
- Here, [tex]\( m = -\frac{2}{3} \)[/tex], [tex]\( x_1 = -3 \)[/tex], and [tex]\( y_1 = 1 \)[/tex].
4. Substitute the values into the point-slope form:
- Using the given point [tex]\((-3,1)\)[/tex]:
[tex]\[ y - 1 = -\frac{2}{3}(x - (-3)) \][/tex]
- Simplifying the expression inside the parentheses:
[tex]\[ y - 1 = -\frac{2}{3}(x + 3) \][/tex]
Therefore, the equation of the line that is parallel to the given line and passes through the point [tex]\((-3,1)\)[/tex] is:
[tex]\[ y - 1 = -\frac{2}{3}(x + 3) \][/tex]
The correct answer is:
[tex]\[ y-1=-\frac{2}{3}(x+3) \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.