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line c can be written as y= 3/4x-2 .line d which is perpendicular includes the point (6,-3). what is the equation of line d?

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Final answer:

The equation of line d, which is perpendicular to line c (y = 3/4x - 2) and passes through the point (6, -3), is y = (-4/3)x + 5.

Step-by-step explanation:

To find the equation of line d which is perpendicular to line c with the equation y = 3/4x - 2, we must first determine the slope of line d.

Since line d is perpendicular to line c, its slope will be the negative reciprocal of the slope of line c. So, the slope of line c is 3/4, which means the slope of line d will be -4/3.

Next, we use the point-slope form of a line to construct the equation for line d.

The point-slope form is given by (y - y1) = m(x - x1), where (x1, y1) is the point through which the line passes and m is the slope of the line.

Plugging in the given point (6, -3) and the slope -4/3, we get:

(y - (-3)) = (-4/3)(x - 6), which simplifies to y + 3 = (-4/3)x + 8.

Subtracting 3 from both sides gives us the final equation of line d: y = (-4/3)x + 5.

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