Question

Find the equation in terms of X of the line through the points -3,5 and 2,4

Answer 1

`\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-5}{2-(-3)}\implies \cfrac{4-5}{2+3}\implies \cfrac{-1}{5} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-5=-\cfrac{1}{5}[x-(-3)] \implies y-5=-\cfrac{1}{5}(x+3) \\\\\\ y-5=-\cfrac{1}{5}x-\cfrac{3}{5}\implies y=-\cfrac{1}{5}x-\cfrac{3}{5}+5\implies y=-\cfrac{1}{5}x+\cfrac{22}{5}`