Slope-intercept form for the line that passes through (-1,-7) and is perpendicular to the graph of 3x+12y=-6

Step-by-step explanation:

We first need to find the slope of the given line.  Putting that standard form of a line into slope intercept:

12y = -3x - 6 so

In this form we can easily determine that our slope is -1/4.  That means that the perpendicular slope, the opposite reciprocal, is +4.  We will write first the point slope of the new line using our given point, then solve it for y, putting it into slope-intercept form.  y - (-7) = 4(x - (-1)) and

y + 7 = 4x + 4 so

y = 4x + 4 - 7 so

y = 4x - 3