Final answer:
The slope of a line perpendicular to the equation ax + by = c is the negative reciprocal of the original line's slope. Since the equation rearranges to y = (-a/b)x + (c/b), the slope of the original line is -a/b, making the perpendicular slope -b/a, which is answer D.
Step-by-step explanation:
The student has asked about the slope of the line perpendicular to the equation ax + by = c. First, we need to understand that the slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. For the given equation ax + by = c, we first have to rearrange it into the slope-intercept form. This can be done by solving for y to get y = (-a/b)x + (c/b), where the slope of the line represented by the equation ax + by = c is -a/b.
Now, the slope of a line that is perpendicular to another is the negative reciprocal of the original line's slope. Therefore, the slope of the line perpendicular to the given equation would be the negative reciprocal of -a/b, which is b/a. Since the perpendicular slope needs to be the negative reciprocal, the correct answer is D) -b/a.
To summarize, for a line in the form ax + by = c, if it has a slope, say m1, then the slope of a line perpendicular to it, m2, would satisfy m1 × m2 = -1 because perpendicular lines have slopes that are negative reciprocals of each other. Thus, the slope of the perpendicular line is -b/a.