Final answer:
To find the original equation, we can use the information given about the parallel and perpendicular equations. For the parallel equation going through (6,7), the equation will have the same slope as the original equation. For the perpendicular equation going through (-1,2), the equation will have a negative reciprocal slope of the original equation.
Step-by-step explanation:
To find the original equation, we can use the information given about the parallel and perpendicular equations.
For the parallel equation going through (6,7), the equation will have the same slope as the original equation. We can determine the slope by finding the difference in y-values over the difference in x-values: (7 - y) / (6 - x).
For the perpendicular equation going through (-1,2), the equation will have a negative reciprocal slope of the original equation. We can determine the slope by taking the negative reciprocal of the original slope. The equation will be: (y - 2) / (x - (-1)).