so the line goes through 2,2, and the y-intercept, well, a y-intercept is when the graph touches or "intercepts" the y-axis, and when that happens, x = 0, so the point is x = 0, y = 6, or 0,6, therefore
[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&&(~ 2 &,& 2~)
&&(~ 0 &,& 6~)
\end{array}
\\\\\\
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-2}{0-2}\implies \cfrac{4}{-2}\implies -2
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=-2(x-2)
\\\\\\
y-2=-2x+4\implies y=-2x+6[/tex]
