if we look at the equation y = -2x - 1, is already in slope-intercept form, therefore, [tex] \bf y=\stackrel{slope}{-2}x-1 [/tex] has a slope of -2.
now, parallel lines have exactly equal slopes, therefore a parallel to that one above, will have also a slope of -2, so we're really looking for a line whose slope is -2 and runs through -1, 7.
[tex] \bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{7})\qquad \qquad \qquad slope = m\implies -2\\\\\\\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-7=-2[x-(-1)]\\\\\\y-7=-2(x+1)\implies y-7=-2x-2\implies y=-2x+5 [/tex]
