Answer:
3rd option, [tex]y-1 = \frac{1}{2} (x-5)[/tex]
Step-by-step explanation:
To find out which option is correct, we can write the equation in point-slope form ourselves.
Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write the equation in point-slope form. Substitute the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.
Since [tex]m[/tex] represents the slope, substitute [tex]\frac{1}{2}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (5,1) into the formula as well. Substitute 5 for [tex]x_1[/tex] and 1 for [tex]y_1[/tex]. This gives the following equation:
[tex]y-1 = \frac{1}{2} (x-5)[/tex]
