Find the equation of a line that goes through the point ( - 3, - 1 ) and is perpendicular to the line: y = - 1 / 4x - 1.

Step 1: Find the slope of the given line

The equation of the given line is in the form y = mx + c, where m is the slope. So, the slope of the given line is -1/4.

Step 2: Find the slope of the line perpendicular to the given line

The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. So, the slope of the line we are trying to find is -1/(-1/4) = 4.

Step 3: Use the point-slope form of a line to find the equation of the line

The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the given point (-3, -1) and the slope we found in step 2, we get:

y - (-1) = 4(x - (-3))

Step 4: Simplify the equation

Simplifying the equation gives us:

y + 1 = 4x + 12

Subtract 1 from both sides to get the equation in slope-intercept form (y = mx + c):

y = 4x + 11

So, the equation of the line that goes through the point (-3, -1) and is perpendicular to the line y = -1/4x - 1 is y = 4x + 11.