Question

Complete the point-slope equation of the line through (-5,4) and (1,6)
y-6=????

Answer 1

`\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{6}) \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-4}{1-(-5)}\implies \cfrac{6-4}{1+5}\implies \cfrac{2}{6}\implies \cfrac{1}{3} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_2= m(x- x_2)}\implies y-6=\cfrac{1}{3}(x-1)`

bearing in mnd that for the point-slope form, you can always fill it in with either x₁, y₁, or x₂, y₂, either one will do.