Question

type the slope intercept equation of the line that passes through the point (1,1)&(7,4) enter fraction in simplest form

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ 1}})\quad % (c,d) &({{ 7}}\quad ,&{{ 4}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{4-1}{7-1}\implies \cfrac{3}{6}\implies \cfrac{1}{2}$

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-1=\cfrac{1}{2}(x-1)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-1=\cfrac{1}{2}x-\cfrac{1}{2}\implies y=\cfrac{1}{2}x-\cfrac{1}{2}+1\implies y=\cfrac{1}{2}x+\cfrac{1}{2}$