Final answer:
To write the equation of Line C in point slope form, we use the perpendicularity of Line C and Line A and the given point (4,-6). We find the slope of Line C by taking the negative reciprocal of the slope of Line A. Substituting the point and the slope into the point-slope form equation gives us the equation y + 6 = -1/m(x - 4).
Step-by-step explanation:
To write the equation of a line in point-slope form, we need a point on the line and the slope of the line. In this case, the point given is (4, -6). Since line C is perpendicular to line A, the slopes of the two lines are negative reciprocals of each other. Let's assume the slope of line A is m. The slope of line C is then -1/m.
Now, let's substitute the point (4, -6) and the slope -1/m into the point-slope form equation y - y1 = m(x - x1). We get: y - (-6) = -1/m(x - 4), which simplifies to y + 6 = -1/m(x - 4).
Therefore, the equation of line C in point-slope form is: y + 6 = -1/m(x - 4).
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