Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
To find the equation of a line that is parallel to a given line and passes through a specific point, we will follow these steps:
1. Identify the slope of the given line:
The given line has the equation [tex]\( y = \frac{1}{5}x + 4 \)[/tex]. The slope of this line, [tex]\( m \)[/tex], is the coefficient of [tex]\( x \)[/tex], which is [tex]\( \frac{1}{5} \)[/tex].
2. Determine the slope of the parallel line:
Parallel lines have the same slope. Therefore, the slope of the line we need to find is also [tex]\( \frac{1}{5} \)[/tex].
3. Use the point-slope form of the line equation:
The point-slope form of a line's equation is [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is a point on the line.
Here, we are given the point [tex]\((-2, 2)\)[/tex] and the slope [tex]\( m = \frac{1}{5} \)[/tex].
So, we substitute these values into the point-slope form:
[tex]\[ y - 2 = \frac{1}{5}(x + 2) \][/tex]
4. Solve for [tex]\( y \)[/tex] to get the slope-intercept form:
Simplify the equation:
[tex]\[ y - 2 = \frac{1}{5}x + \frac{1}{5} \cdot 2 \][/tex]
[tex]\[ y - 2 = \frac{1}{5}x + \frac{2}{5} \][/tex]
Add 2 to both sides to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{1}{5}x + \frac{2}{5} + 2 \][/tex]
[tex]\[ y = \frac{1}{5}x + \frac{2}{5} + \frac{10}{5} \][/tex]
[tex]\[ y = \frac{1}{5}x + \frac{12}{5} \][/tex]
5. Compare with the given choices:
We need to determine which of the provided choices matches [tex]\( y = \frac{1}{5}x + \frac{12}{5} \)[/tex]:
- [tex]\( y = \frac{1}{5}x + 4 \)[/tex]
- [tex]\( y = \frac{1}{5}x + \frac{12}{5} \)[/tex]
- [tex]\( y = -5x + 4 \)[/tex]
- [tex]\( y = -5x + \frac{12}{5} \)[/tex]
The equation of the line that is parallel to the given line and passes through the point [tex]\((-2, 2)\)[/tex] is [tex]\( y = \frac{1}{5}x + \frac{12}{5} \)[/tex].
Comparing this with the choices given, we find that the correct answer is:
[tex]\[ \boxed{2} \][/tex]
1. Identify the slope of the given line:
The given line has the equation [tex]\( y = \frac{1}{5}x + 4 \)[/tex]. The slope of this line, [tex]\( m \)[/tex], is the coefficient of [tex]\( x \)[/tex], which is [tex]\( \frac{1}{5} \)[/tex].
2. Determine the slope of the parallel line:
Parallel lines have the same slope. Therefore, the slope of the line we need to find is also [tex]\( \frac{1}{5} \)[/tex].
3. Use the point-slope form of the line equation:
The point-slope form of a line's equation is [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is a point on the line.
Here, we are given the point [tex]\((-2, 2)\)[/tex] and the slope [tex]\( m = \frac{1}{5} \)[/tex].
So, we substitute these values into the point-slope form:
[tex]\[ y - 2 = \frac{1}{5}(x + 2) \][/tex]
4. Solve for [tex]\( y \)[/tex] to get the slope-intercept form:
Simplify the equation:
[tex]\[ y - 2 = \frac{1}{5}x + \frac{1}{5} \cdot 2 \][/tex]
[tex]\[ y - 2 = \frac{1}{5}x + \frac{2}{5} \][/tex]
Add 2 to both sides to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{1}{5}x + \frac{2}{5} + 2 \][/tex]
[tex]\[ y = \frac{1}{5}x + \frac{2}{5} + \frac{10}{5} \][/tex]
[tex]\[ y = \frac{1}{5}x + \frac{12}{5} \][/tex]
5. Compare with the given choices:
We need to determine which of the provided choices matches [tex]\( y = \frac{1}{5}x + \frac{12}{5} \)[/tex]:
- [tex]\( y = \frac{1}{5}x + 4 \)[/tex]
- [tex]\( y = \frac{1}{5}x + \frac{12}{5} \)[/tex]
- [tex]\( y = -5x + 4 \)[/tex]
- [tex]\( y = -5x + \frac{12}{5} \)[/tex]
The equation of the line that is parallel to the given line and passes through the point [tex]\((-2, 2)\)[/tex] is [tex]\( y = \frac{1}{5}x + \frac{12}{5} \)[/tex].
Comparing this with the choices given, we find that the correct answer is:
[tex]\[ \boxed{2} \][/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.