Question

the formula y-y1 =m(x-x1) is the pot slope form of the equation of a line where m is the slope of the line and(x,y) and (x1,y1) are points of the line. Solve the equation for m, and e slope of a line that6 includes the poits (4,-2) and (5,0).

Answer 1

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ 4}} &,&{{ -2}}~) % (c,d) &&(~{{ 5}} &,&{{ 0}}~) \end{array} \\\\\\ % slope = m slope = {{ m}}\implies \cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{5-(-2)}{0-4}\implies \cfrac{5+2}{0-4}\implies -\cfrac{7}{4}$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-2)=-\cfrac{7}{4}(x-4) \\\\\\ y+2=-\cfrac{7}{4}(x-4)\implies y+2=-\cfrac{7}{4}x+7\implies y=-\cfrac{7}{4}x+9$