Question

What is the equation of the line that passes through the points (-2,2) and (0,5)

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ 2}})\quad % (c,d) &({{ 0}}\quad ,&{{ 5}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{5-2}{0-(-2)}\implies \cfrac{5-2}{0+2} \\\\\\ \cfrac{3}{2}$

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=\cfrac{3}{2}(x-(-2))\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-2=\cfrac{3}{2}(x+2)\implies y-2=\cfrac{3}{2}x+3\implies y=\cfrac{3}{2}x+3+2 \\\\\\ y=\cfrac{3}{2}x+5$