Final answer:
The equation of the line perpendicular to the line 3x + 8y = -16 and passing through the point (-3, -3) is y = (8/3)x - 8.
Step-by-step explanation:
To find the equation of a line perpendicular to the line 3x + 8y = -16 and passing through the point (-3, -3), we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given equation can be rewritten in slope-intercept form as y = -(3/8)x - 2. To find the slope of this line, we compare it to the standard slope-intercept form y = mx + b, where m represents the slope. Therefore, the slope of the given line is -3/8. The negative reciprocal of -3/8 is 8/3. Using the point-slope form of a line, we can now write the equation of the line perpendicular to the given line and passing through the point (-3, -3): y - (-3) = (8/3)(x - (-3)). Simplifying, we have y + 3 = (8/3)(x + 3), which can be rearranged as y = (8/3)x - 8