The line l1 has equation 4y - 3x = 10. Line l2 passes through points (5, -1) and (-1, 8). Determine whether the lines l1 and l2 are parallel, perpendicular or neither.

To determine the answer the gradient of both lines must be found. To find the gradient of line l1 the equation can be rewritten in the form y = mx + c. 4y - 3x = 10 so y = 3/4 x + 5/2. From this equation the gradient of the line is 3/4.
If the two lines are parallel the gradient of l2 will be the same, if they are perpendicular the gradient will be -4/3.
To find the gradient of l2 the difference between the y and x coordinates is found, the gradient is the dy/dx = (-1 - 8) / (5 - -1) = -3/2. As this gradient is not equal to either the gradient of l1 or -4/3 the two lines are neither parallel or perpendicular.