Question

The line through points at (3,4) and (4,6)

Answer 1

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-4}{4-3}\implies \cfrac{2}{1}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=2(x-3) \\\\\\ y-4=2x-6\implies y=2x+1$

Answer 2

The slope is 2.

The equation of the line is y=2x-2

The y-intercept is -2.