Question

Line l passes through the origin and point (3,4).What is the slope of a line parallel to line l

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ 0}})\quad % (c,d) &({{ 3}}\quad ,&{{ 4}})\\ &origin \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{4-0}{3-0}\implies \cfrac{4}{3}$

so, that's the slope of a line passing through the origin and 3,4, and any line parallel to it, will have the same exact slope.