Question

What is the slip-intercept from equation of the line that passes through (3,4) and (5,16)

Answer 1

Assuming you meant the slope-intercept form of course,

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 3 &,& 4~) % (c,d) &&(~ 5 &,& 16~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{16-4}{5-3}\implies \cfrac{12}{2}\implies 6 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-4=6(x-3) \\\\\\ y-4=6x-18\implies y=6x-14$