Question

The graph of a linear function passes through the points (2, 4) and (8, 10).

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ 4}})\quad % (c,d) &({{ 8}}\quad ,&{{ 10}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{10-4}{8-(-2)}\implies \cfrac{10-4}{8+2}\implies \cfrac{6}{10} \\\\\\ \cfrac{3}{5}$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=\cfrac{3}{5}[x-(-2)]\implies y-4=\cfrac{3}{5}(x+2) \\\\\\ y-4=\cfrac{3}{5}x+\cfrac{6}{5}\implies y=\cfrac{3}{5}x+\cfrac{6}{5}+4\implies y=\cfrac{3}{5}x+\cfrac{26}{5}$