Question

Find an equation for the line with the given properties. Express the equation in​ slope-intercept form. Containing the points Upper P equals (-1, 3) and Upper Q equals (1, 0)

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -1}}\quad ,&{{ 3}})\quad % (c,d) &({{ 1}}\quad ,&{{ 0}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{0-3}{1-(-1)}\implies \cfrac{0-3}{1+1} \\\\\\ \cfrac{-3}{2}$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-3=-\cfrac{3}{2}[x-(-1)] \\\\\\ y-3=-\cfrac{3}{2}(x+1)\implies y-3=-\cfrac{3}{2}x-\cfrac{3}{2}\implies y=-\cfrac{3}{2}x-\cfrac{3}{2}+3 \\\\\\ y=-\cfrac{3}{2}x+\cfrac{3}{2}$