Question

What equation in slope intercept form represents the line that passes through the two points? (2, 5), (9, 2) Question 6 options: y = 7/3x + 41/7 y = 3/7x - 41/7 y = -7/3x - 41/7 y = -3/7x + 41/7

Answer 1

$\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-5}{9-2}\implies \cfrac{-3}{7} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-5=-\cfrac{3}{7}(x-2) \implies y-5=-\cfrac{3}{7}x+\cfrac{6}{7} \\\\\\ y=-\cfrac{3}{7}x+\cfrac{6}{7}+5\implies y=-\cfrac{3}{7}x+\cfrac{41}{7}$