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if we look at the equation y = -2x - 1, is already in slope-intercept form, therefore,
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.
![\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](https://tex.z-dn.net/?f=%20%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B-1%7D~%2C~%5Cstackrel%7By_1%7D%7B7%7D%29%5Cqquad%20%5Cqquad%20%5Cqquad%20slope%20%3D%20%20m%5Cimplies%20-2%5C%5C%5C%5C%5C%5C%5Cstackrel%7B%5Ctextit%7Bpoint-slope%20form%7D%7D%7By-%20y_1%3D%20m%28x-%20x_1%29%7D%5Cimplies%20y-7%3D-2%5Bx-%28-1%29%5D%5C%5C%5C%5C%5C%5Cy-7%3D-2%28x%2B1%29%5Cimplies%20y-7%3D-2x-2%5Cimplies%20y%3D-2x%2B5%20)