Final answer:
To determine the equation of a line perpendicular to another line, find the negative reciprocal of the slope of the given line and substitute a point into the equation.
Step-by-step explanation:
To determine the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line has the equation 3x + 4y + 28 = 0. To find the slope of this line, rearrange the equation to the form y = mx + b, where m is the slope. So, 4y = -3x - 28, and y = (-3/4)x - 7.
The slope of this line is -3/4. The negative reciprocal of -3/4 is 4/3. So the slope of the perpendicular line is 4/3. Now, we need to find the equation of the perpendicular line passing through a given point. Let's say the point is (a, b). The equation of the line in point-slope form is y - b = (4/3)(x - a).
In standard form, the equation becomes 3y - 4x + 4a - 3b = 0. This is the equation of the line perpendicular to 3x + 4y + 28 = 0.