Consider the line y = -3/-2 x +6. find the equation of the line that is perpendicular to this line and passes through the point (-9,-3). find the equation of the line that is parallel to this line and passes through the point (-9,-3).

The perpendicular line would be y = -2/3x - 9

The parallel line would be y = 3/2x + 21/2

Step-by-step explanation:

Since we have the slope of 3/2, we know the perpendicular slope will be -2/3. This is because perpendicular lines have opposite and reciprocal slopes. Now we can use that and the point in point-slope form to get the equation.

y - y1 = m(x - x1)

y + 3 = -2/3(x + 9)

y + 3 = -2/3x - 6

y = -2/3x - 9

For the parallel line we would use the same slope as the original (3/2) and also start with point-slope form.

y - y1 = m(x - x1)

y + 3 = 3/2(x + 9)

y + 3 = 3/2x + 27/2

y = 3/2x + 21/2

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step-by-step explanation: