To find the equation of a line passing through the point (-1, -6) and perpendicular to the line 8x - 3y = 24, we need to follow these steps:
1. Determine the slope of the given line 8x - 3y = 24:
Rearrange the equation into slope-intercept form (y = mx + b) by solving for y:
-3y = -8x + 24
y = 8/3x - 8
The slope of this line is 8/3.
2. Determine the slope of the line perpendicular to the given line:
The slope of a line perpendicular to another line is the negative reciprocal of the original slope. So, the slope of the perpendicular line is -3/8.
3. Use the point-slope form of the equation of a line (y - y1 = m(x - x1)) to find the equation of the line:
Substitute the point (-1, -6) and the perpendicular slope -3/8 into the point-slope form:
y - (-6) = -3/8(x - (-1))
y + 6 = -3/8(x + 1)
y + 6 = -3/8x - 3/8
y = -3/8x - 3/8 - 6
y = -3/8x - 27/8
Therefore, the equation of the line passing through the point (-1, -6) and perpendicular to 8x - 3y = 24 is y = -3/8x - 27/8.
