IDNLearn.com is designed to help you find the answers you need quickly and easily. Find the solutions you need quickly and accurately with help from our knowledgeable community.
Sagot :
To determine which equation represents a line passing through the point [tex]\((5, 1)\)[/tex] with a slope of [tex]\(\frac{1}{2}\)[/tex], we should use the point-slope form of the equation of a line. The point-slope form is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope.
Given:
- the point [tex]\((5, 1)\)[/tex] means [tex]\(x_1 = 5\)[/tex] and [tex]\(y_1 = 1\)[/tex]
- the slope [tex]\(m = \frac{1}{2}\)[/tex]
We substitute these values into the point-slope form equation:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]
Therefore, the equation of the line that passes through the point [tex]\((5, 1)\)[/tex] and has a slope of [tex]\(\frac{1}{2}\)[/tex] is:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]
Thus, the correct option is:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]
This matches with the third option:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope.
Given:
- the point [tex]\((5, 1)\)[/tex] means [tex]\(x_1 = 5\)[/tex] and [tex]\(y_1 = 1\)[/tex]
- the slope [tex]\(m = \frac{1}{2}\)[/tex]
We substitute these values into the point-slope form equation:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]
Therefore, the equation of the line that passes through the point [tex]\((5, 1)\)[/tex] and has a slope of [tex]\(\frac{1}{2}\)[/tex] is:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]
Thus, the correct option is:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]
This matches with the third option:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.