Which equation represents a line that passes though (5, 1) and has a slope of 1/2?

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 havethe 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]