Write an equation of the line through (-6,-1) having slope of give the answer in standard form.

Use the point-slope form:  y-k = m(x-h).

Here,  y-[-1]) = (17/14)(x+6), or y+2 = (17/14)(x+6).  This could, of course, be solved for y if you wish.  Mult. both sides by 14, we get 14y+28=17(x+6).

This becomes 17x + 102 - 14y - 28 = 0, or 17x -14y + 74 = 0 (which is standard form).  You could also write 17x - 14y = -74.