Answer:
[tex]\large\boxed{y-1=\dfrac{1}{2}(x-5)\leftarrow\text{point-slope form}}\\\boxed{y=\dfrac{1}{2}x-\dfrac{3}{2}\leftarrow\text{slope-intercept form}}\\\boxed{x-2y=3\leftarrow\text{standard form}}[/tex]
Step-by-step explanation:
The point-slope of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have
the point [tex](5,\ 1)\to x_1=5,\ y_1=1[/tex]
and the slope [tex]m=\dfrac{1}{2}[/tex]
Substitute:
[tex]y-1=\dfrac{1}{2}(x-5)[/tex] use distributive property
[tex]y-1=\dfrac{1}{2}x-\dfrac{5}{2}[/tex] add 1 to both sides
[tex]y=\dfrac{1}{2}x-\dfrac{3}{2}[/tex] multiply both sides by 2
[tex]2y=x-3[/tex] subtract x from both sides
[tex]-x+2y=-3[/tex] change the signs
[tex]x-2y=3[/tex]
