Certainly! Let's find the equation of a line that passes through the point \((5,1)\) and has a slope of \(\frac{1}{2}\).
We will use the point-slope form of the equation of a line, which is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here, \((x_1, y_1)\) is a point on the line and \(m\) is the slope.
Given:
- The point \((x_1, y_1) = (5, 1)\)
- The slope \(m = \frac{1}{2}\)
Substitute the values into the point-slope form:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]
This equation represents the line that passes through the point \((5,1)\) and has a slope of \(\frac{1}{2}\).
Among the given choices, the one that matches this equation is:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]
Thus, the correct answer is:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]
So, the corresponding choice is:
[tex]\[ \boxed{3} \][/tex]
