Answer:
Case 1: 7y + x - 20 = 0 (Perpendicular)
Case 2: y - 7x + 40 = 0 (Parallel)
Step-by-step explanation:
Case 1: Perpendicular
Equation of the given line y = 7x - 6
Comparing with the general equation y = mx + c; m = 7
For two lines to be perpendicular, the product of their gradients is (-1) or we can also say; gradient of one line must be the negative inverse of the other gradient.
So the gradient of a line perpendicular to y = 7x - 6 should be (-1/7)
Now solving for the equation of the line using the formula
y - y = m(x - x ) where (x , y ) are the coordinates of the point.
substituting..
y - 2 = (-1/7)(x - 6)
7(y - 2) = -1(x - 6)
7y - 14 = -x + 6
7y + x -14 - 6 = 0
7y + x - 20 = 0 is the equation of the line perpendicular to y = 7x - 6 and passes through the point (6,2)
Case 2: Parallel
Equation of the given line y = 7x - 6
Comparing with the general equation y = mx + c; m = 7
For two lines to be parallel, they must have equal gradients.
So the gradient of a line parallel to y = 7x - 6 should be 7
Now solving for the equation of the line using the formula
y - y = m(x - x ) where (x , y ) are the coordinates of the point.
substituting..
y - 2 = 7(x - 6)
y - 2 = 7x - 42
y - 7x -2 + 42 = 0
y - 7x + 40 = 0 is the equation of the line parallel to y = 7x - 6 and passes through the point (6,2)
