Question

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

Answer 1

The answer is c  because
 when you y -1 = ( x - 5)
                 1- 1 = 5 -5
                   0 = 0
where  A    y - 5 = ( x - 1)
                  1 - 5 =  ( 5 - 1 )
                    -4 dosenot equal 4

Answer 2

$\bf \begin{array}{lllll} &x_1&y_1\\ &({{ 5}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{1}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=\cfrac{1}{2}(x-5)\implies y-1=\cfrac{1}{2}x-\cfrac{5}{2} \\\\\\ y=\cfrac{1}{2}x-\cfrac{5}{2}+1\implies y=\cfrac{1}{2}x-\cfrac{3}{2}$