Question

What is the equation of the line that passes through the point (-1,7) and is parallel to the line y= -2x-1

Answer 1

if we look at the equation y = -2x - 1, is already in slope-intercept form, therefore, $\bf y=\stackrel{slope}{-2}x-1$ 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.

$\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{7})\qquad \qquad \qquad slope = m\implies -2\\\\\\\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-7=-2[x-(-1)]\\\\\\y-7=-2(x+1)\implies y-7=-2x-2\implies y=-2x+5$