Question

Find a general linear equation Ax+By+C=0 of the straight line that passes through the point (1,1) and has slope 1/5.

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 1}}\quad ,&{{ 1}})\quad % (c,d) \end{array} \\\quad \\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies\cfrac{1}{5} \\ \quad \\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad \begin{array}{llll} \textit{plug in the values}\\ \textit{and move everything to}\\ \textit{the left-side} \end{array}\\ \qquad \uparrow\\ \textit{point-slope form}$