Question

Line JK passes through points J(–4, –5) and K(–6, 3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?

Answer 1

$\bf J(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-5})\qquad K(\stackrel{x_2}{-6}~,~\stackrel{y_2}{3}) \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-(-5)}{-6-(-4)}\implies \cfrac{3+5}{-6+4}\implies -4 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-5)=-4[x-(-4)] \\\\\\ y+5=-4(x+4)\implies y+5=-4x-16\implies y=\stackrel{m}{-4}x\stackrel{b}{-21}$