Question

What is the equation of the line passing through (0,0) and (1,4)

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ 0}})\quad % (c,d) &({{ 1}}\quad ,&{{ 4}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{4-0}{1-0}\implies 4$

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-0=4(x-0)\implies \boxed{y=4x} \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form}$